Document

**Published in:** LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications.

Udi Boker, Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç. Safety and Liveness of Quantitative Automata. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{boker_et_al:LIPIcs.CONCUR.2023.17, author = {Boker, Udi and Henzinger, Thomas A. and Mazzocchi, Nicolas and Sara\c{c}, N. Ege}, title = {{Safety and Liveness of Quantitative Automata}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {17:1--17:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-299-0}, ISSN = {1868-8969}, year = {2023}, volume = {279}, editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.17}, URN = {urn:nbn:de:0030-drops-190118}, doi = {10.4230/LIPIcs.CONCUR.2023.17}, annote = {Keywords: quantitative safety, quantitative liveness, quantitative automata} }

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**Published in:** LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

We introduce hypernode automata as a new specification formalism for hyperproperties of concurrent systems. They are finite automata with nodes labeled with hypernode logic formulas and transitions labeled with actions. A hypernode logic formula specifies relations between sequences of variable values in different system executions. Unlike HyperLTL, hypernode logic takes an asynchronous view on execution traces by constraining the values and the order of value changes of each variable without correlating the timing of the changes. Different execution traces are synchronized solely through the transitions of hypernode automata. Hypernode automata naturally combine asynchronicity at the node level with synchronicity at the transition level. We show that the model-checking problem for hypernode automata is decidable over action-labeled Kripke structures, whose actions induce transitions of the specification automata. For this reason, hypernode automaton is a suitable formalism for specifying and verifying asynchronous hyperproperties, such as declassifying observational determinism in multi-threaded programs.

Ezio Bartocci, Thomas A. Henzinger, Dejan Nickovic, and Ana Oliveira da Costa. Hypernode Automata. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bartocci_et_al:LIPIcs.CONCUR.2023.21, author = {Bartocci, Ezio and Henzinger, Thomas A. and Nickovic, Dejan and Oliveira da Costa, Ana}, title = {{Hypernode Automata}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {21:1--21:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-299-0}, ISSN = {1868-8969}, year = {2023}, volume = {279}, editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.21}, URN = {urn:nbn:de:0030-drops-190153}, doi = {10.4230/LIPIcs.CONCUR.2023.21}, annote = {Keywords: Hyperproperties, Asynchronous, Automata, Logic} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time.

Thomas A. Henzinger, Pavol Kebis, Nicolas Mazzocchi, and N. Ege Saraç. Regular Methods for Operator Precedence Languages. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 129:1-129:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{henzinger_et_al:LIPIcs.ICALP.2023.129, author = {Henzinger, Thomas A. and Kebis, Pavol and Mazzocchi, Nicolas and Sara\c{c}, N. Ege}, title = {{Regular Methods for Operator Precedence Languages}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {129:1--129:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.129}, URN = {urn:nbn:de:0030-drops-181814}, doi = {10.4230/LIPIcs.ICALP.2023.129}, annote = {Keywords: operator precedence automata, syntactic congruence, antichain algorithm} }

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**Published in:** LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

We explore the notion of history-determinism in the context of timed automata (TA). History-deterministic automata are those in which nondeterminism can be resolved on the fly, based on the run constructed thus far. History-determinism is a robust property that admits different game-based characterisations, and history-deterministic specifications allow for game-based verification without an expensive determinization step.
We show yet another characterisation of history-determinism in terms of fair simulation, at the general level of labelled transition systems: a system is history-deterministic precisely if and only if it fairly simulates all language smaller systems.
For timed automata over infinite timed words it is known that universality is undecidable for Büchi TA. We show that for history-deterministic TA with arbitrary parity acceptance, timed universality, inclusion, and synthesis all remain decidable and are ExpTime-complete.
For the subclass of TA with safety or reachability acceptance, we show that checking whether such an automaton is history-deterministic is decidable (in ExpTime), and history-deterministic TA with safety acceptance are effectively determinizable without introducing new automata states.

Thomas A. Henzinger, Karoliina Lehtinen, and Patrick Totzke. History-Deterministic Timed Automata. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{henzinger_et_al:LIPIcs.CONCUR.2022.14, author = {Henzinger, Thomas A. and Lehtinen, Karoliina and Totzke, Patrick}, title = {{History-Deterministic Timed Automata}}, booktitle = {33rd International Conference on Concurrency Theory (CONCUR 2022)}, pages = {14:1--14:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-246-4}, ISSN = {1868-8969}, year = {2022}, volume = {243}, editor = {Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.14}, URN = {urn:nbn:de:0030-drops-170778}, doi = {10.4230/LIPIcs.CONCUR.2022.14}, annote = {Keywords: Timed Automata, History-determinism, Good-for-games, fair simulation, synthesis} }

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Invited Talk

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We summarize how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.

Guy Avni and Thomas A. Henzinger. An Updated Survey of Bidding Games on Graphs (Invited Talk). In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 3:1-3:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{avni_et_al:LIPIcs.MFCS.2022.3, author = {Avni, Guy and Henzinger, Thomas A.}, title = {{An Updated Survey of Bidding Games on Graphs}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {3:1--3:6}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.3}, URN = {urn:nbn:de:0030-drops-168017}, doi = {10.4230/LIPIcs.MFCS.2022.3}, annote = {Keywords: Bidding games, Richman bidding, poorman bidding, mean-payoff, parity} }

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Invited Paper

**Published in:** LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and study their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We show how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.

Guy Avni and Thomas A. Henzinger. A Survey of Bidding Games on Graphs (Invited Paper). In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{avni_et_al:LIPIcs.CONCUR.2020.2, author = {Avni, Guy and Henzinger, Thomas A.}, title = {{A Survey of Bidding Games on Graphs}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {2:1--2:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-160-3}, ISSN = {1868-8969}, year = {2020}, volume = {171}, editor = {Konnov, Igor and Kov\'{a}cs, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.2}, URN = {urn:nbn:de:0030-drops-128147}, doi = {10.4230/LIPIcs.CONCUR.2020.2}, annote = {Keywords: Bidding games, Richman bidding, poorman bidding, mean-payoff, parity} }

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**Published in:** LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2020.23, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {23:1--23:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-160-3}, ISSN = {1868-8969}, year = {2020}, volume = {171}, editor = {Konnov, Igor and Kov\'{a}cs, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.23}, URN = {urn:nbn:de:0030-drops-128359}, doi = {10.4230/LIPIcs.CONCUR.2020.23}, annote = {Keywords: vector addition systems, mean-payoff, multidimension, probabilistic semantics} }

Document

**Published in:** LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

The monitoring of event frequencies can be used to recognize behavioral anomalies, to identify trends, and to deduce or discard hypotheses about the underlying system. For example, the performance of a web server may be monitored based on the ratio of the total count of requests from the least and most active clients. Exact frequency monitoring, however, can be prohibitively expensive; in the above example it would require as many counters as there are clients. In this paper, we propose the efficient probabilistic monitoring of common frequency properties, including the mode (i.e., the most common event) and the median of an event sequence. We define a logic to express composite frequency properties as a combination of atomic frequency properties. Our main contribution is an algorithm that, under suitable probabilistic assumptions, can be used to monitor these important frequency properties with four counters, independent of the number of different events. Our algorithm samples longer and longer subwords of an infinite event sequence. We prove the almost-sure convergence of our algorithm by generalizing ergodic theory from increasing-length prefixes to increasing-length subwords of an infinite sequence. A similar algorithm could be used to learn a connected Markov chain of a given structure from observing its outputs, to arbitrary precision, for a given confidence.

Thomas Ferrère, Thomas A. Henzinger, and Bernhard Kragl. Monitoring Event Frequencies. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ferrere_et_al:LIPIcs.CSL.2020.20, author = {Ferr\`{e}re, Thomas and Henzinger, Thomas A. and Kragl, Bernhard}, title = {{Monitoring Event Frequencies}}, booktitle = {28th EACSL Annual Conference on Computer Science Logic (CSL 2020)}, pages = {20:1--20:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-132-0}, ISSN = {1868-8969}, year = {2020}, volume = {152}, editor = {Fern\'{a}ndez, Maribel and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.20}, URN = {urn:nbn:de:0030-drops-116633}, doi = {10.4230/LIPIcs.CSL.2020.20}, annote = {Keywords: monitoring, frequency property, Markov chain} }

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**Published in:** LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

In two-player games on graphs, the players move a token through a graph to produce a finite or infinite path, which determines the qualitative winner or quantitative payoff of the game. We study bidding games in which the players bid for the right to move the token. Several bidding rules were studied previously. In Richman bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Poorman bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. Taxman bidding spans the spectrum between Richman and poorman bidding. They are parameterized by a constant tau in [0,1]: portion tau of the winning bid is paid to the other player, and portion 1-tau to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games. It was previously shown that both Richman and poorman infinite-duration games with qualitative objectives reduce to reachability games, and we show a similar result here. Our most interesting results concern quantitative taxman games, namely mean-payoff games, where poorman and Richman bidding differ significantly. A central quantity in these games is the ratio between the two players' initial budgets. While in poorman mean-payoff games, the optimal payoff of a player depends on the initial ratio, in Richman bidding, the payoff depends only on the structure of the game. In both games the optimal payoffs can be found using (different) probabilistic connections with random-turn games in which in each turn, instead of bidding, a coin is tossed to determine which player moves. While the value with Richman bidding equals the value of a random-turn game with an un-biased coin, with poorman bidding, the bias in the coin is the initial ratio of the budgets. We give a complete classification of mean-payoff taxman games that is based on a probabilistic connection: the value of a taxman bidding game with parameter tau and initial ratio r, equals the value of a random-turn game that uses a coin with bias F(tau, r) = (r+tau * (1-r))/(1+tau). Thus, we show that Richman bidding is the exception; namely, for every tau <1, the value of the game depends on the initial ratio. Our proof technique simplifies and unifies the previous proof techniques for both Richman and poorman bidding.

Guy Avni, Thomas A. Henzinger, and Đorđe Žikelić. Bidding Mechanisms in Graph Games. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{avni_et_al:LIPIcs.MFCS.2019.11, author = {Avni, Guy and Henzinger, Thomas A. and \v{Z}ikeli\'{c}, {\D}or{\d}e}, title = {{Bidding Mechanisms in Graph Games}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {11:1--11:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.11}, URN = {urn:nbn:de:0030-drops-109553}, doi = {10.4230/LIPIcs.MFCS.2019.11}, annote = {Keywords: Bidding games, Richman bidding, poorman bidding, taxman bidding, mean-payoff games, random-turn games} }

Document

**Published in:** LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a non-terminating system and its environment. In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Bidding games are known to have a clean and elegant mathematical structure that relies on the ability of the players to submit arbitrarily small bids. Many applications, however, require a fixed granularity for the bids, which can represent, for example, the monetary value expressed in cents. We study, for the first time, the combination of discrete-bidding and infinite-duration games. Our most important result proves that these games form a large determined subclass of concurrent games, where determinacy is the strong property that there always exists exactly one player who can guarantee winning the game. In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games. We study several natural tie-breaking mechanisms and show that, while some do not admit determinacy, most natural mechanisms imply determinacy for every pair of initial budgets.

Milad Aghajohari, Guy Avni, and Thomas A. Henzinger. Determinacy in Discrete-Bidding Infinite-Duration Games. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{aghajohari_et_al:LIPIcs.CONCUR.2019.20, author = {Aghajohari, Milad and Avni, Guy and Henzinger, Thomas A.}, title = {{Determinacy in Discrete-Bidding Infinite-Duration Games}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {20:1--20:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-121-4}, ISSN = {1868-8969}, year = {2019}, volume = {140}, editor = {Fokkink, Wan and van Glabbeek, Rob}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.20}, URN = {urn:nbn:de:0030-drops-109226}, doi = {10.4230/LIPIcs.CONCUR.2019.20}, annote = {Keywords: Bidding games, Richman games, determinacy, concurrent games, discrete bidding} }

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**Published in:** LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Long-Run Average Behavior of Vector Addition Systems with States. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2019.27, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Long-Run Average Behavior of Vector Addition Systems with States}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {27:1--27:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-121-4}, ISSN = {1868-8969}, year = {2019}, volume = {140}, editor = {Fokkink, Wan and van Glabbeek, Rob}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.27}, URN = {urn:nbn:de:0030-drops-109293}, doi = {10.4230/LIPIcs.CONCUR.2019.27}, annote = {Keywords: vector addition systems, mean-payoff, Diophantine inequalities} }

Document

**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Synchronous programs are easy to specify because the side effects of an operation are finished by the time the invocation of the operation returns to the caller. Asynchronous programs, on the other hand, are difficult to specify because there are side effects due to pending computation scheduled as a result of the invocation of an operation. They are also difficult to verify because of the large number of possible interleavings of concurrent computation threads. We present synchronization, a new proof rule that simplifies the verification of asynchronous programs by introducing the fiction, for proof purposes, that asynchronous operations complete synchronously. Synchronization summarizes an asynchronous computation as immediate atomic effect. Modular verification is enabled via pending asynchronous calls in atomic summaries, and a complementary proof rule that eliminates pending asynchronous calls when components and their specifications are composed. We evaluate synchronization in the context of a multi-layer refinement verification methodology on a collection of benchmark programs.

Bernhard Kragl, Shaz Qadeer, and Thomas A. Henzinger. Synchronizing the Asynchronous. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kragl_et_al:LIPIcs.CONCUR.2018.21, author = {Kragl, Bernhard and Qadeer, Shaz and Henzinger, Thomas A.}, title = {{Synchronizing the Asynchronous}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {21:1--21:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.21}, URN = {urn:nbn:de:0030-drops-95591}, doi = {10.4230/LIPIcs.CONCUR.2018.21}, annote = {Keywords: concurrent programs, asynchronous programs, deductive verification, refinement, synchronization, mover types, atomic action, commutativity, Lipton reduction} }

Document

**Published in:** LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Nested weighted automata (NWA) present a robust and convenient automata-theoretic formalism for quantitative specifications.
Previous works have considered NWA that processed input words only in the forward direction. It is natural to allow the automata to process input words backwards as well, for example, to measure the maximal or average time between a response and the preceding request. We therefore introduce and study bidirectional NWA that can process input
words in both directions. First, we show that bidirectional NWA can express interesting quantitative properties that are not expressible by forward-only NWA. Second, for the fundamental decision problems of emptiness and universality, we establish decidability and complexity results for the new framework which match the best-known results for the special case of forward-only NWA. Thus, for NWA, the increased expressiveness of bidirectionality is achieved at no additional computational complexity. This is in stark contrast to the unweighted case, where bidirectional finite automata are no more expressive but exponentially more succinct than their forward-only counterparts.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Bidirectional Nested Weighted Automata. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2017.5, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Bidirectional Nested Weighted Automata}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {5:1--5:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-048-4}, ISSN = {1868-8969}, year = {2017}, volume = {85}, editor = {Meyer, Roland and Nestmann, Uwe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.5}, URN = {urn:nbn:de:0030-drops-77763}, doi = {10.4230/LIPIcs.CONCUR.2017.5}, annote = {Keywords: weighted automata, nested weighted automata, complexity, bidirectional} }

Document

**Published in:** LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to $1$. In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games [Lazarus1999,Lazarus2012]. There, a central question is the existence and computation of threshold budgets; namely, a value t \in [0,1] such that if \PO's budget exceeds t, he can win the game, and if \PT's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games.

Guy Avni, Thomas A. Henzinger, and Ventsislav Chonev. Infinite-Duration Bidding Games. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{avni_et_al:LIPIcs.CONCUR.2017.21, author = {Avni, Guy and Henzinger, Thomas A. and Chonev, Ventsislav}, title = {{Infinite-Duration Bidding Games}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {21:1--21:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-048-4}, ISSN = {1868-8969}, year = {2017}, volume = {85}, editor = {Meyer, Roland and Nestmann, Uwe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.21}, URN = {urn:nbn:de:0030-drops-77741}, doi = {10.4230/LIPIcs.CONCUR.2017.21}, annote = {Keywords: Bidding Games, Parity Games, Mean-Payoff Games, Richman Games} }

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**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

The semantics of concurrent data structures is usually given by a sequential specification and a consistency condition. Linearizability is the most popular consistency condition due to its simplicity and general applicability. Nevertheless, for applications that do not require all guarantees offered by linearizability, recent research has focused on improving performance and scalability of concurrent data structures by relaxing their semantics.
In this paper, we present local linearizability, a relaxed consistency
condition that is applicable to container-type concurrent data
structures like pools, queues, and stacks. While linearizability requires that the effect of each operation is observed by all threads at the same time, local linearizability only requires that for each thread T, the effects of its local insertion operations and the effects of those removal operations that remove values inserted by T are observed by all threads at the same time. We investigate theoretical and practical properties of local linearizability and its relationship to many existing consistency conditions. We present a generic implementation method for locally linearizable data structures that uses existing linearizable data structures as building blocks. Our implementations show performance and scalability improvements over the original building blocks and outperform the fastest existing container-type implementations.

Andreas Haas, Thomas A. Henzinger, Andreas Holzer, Christoph M. Kirsch, Michael Lippautz, Hannes Payer, Ali Sezgin, Ana Sokolova, and Helmut Veith. Local Linearizability for Concurrent Container-Type Data Structures. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{haas_et_al:LIPIcs.CONCUR.2016.6, author = {Haas, Andreas and Henzinger, Thomas A. and Holzer, Andreas and Kirsch, Christoph M. and Lippautz, Michael and Payer, Hannes and Sezgin, Ali and Sokolova, Ana and Veith, Helmut}, title = {{Local Linearizability for Concurrent Container-Type Data Structures}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {6:1--6:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.6}, URN = {urn:nbn:de:0030-drops-61809}, doi = {10.4230/LIPIcs.CONCUR.2016.6}, annote = {Keywords: (concurrent) data structures, relaxed semantics, linearizability} }

Document

**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results.

Przemyslaw Daca, Thomas A. Henzinger, Jan Kretinsky, and Tatjana Petrov. Linear Distances between Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{daca_et_al:LIPIcs.CONCUR.2016.20, author = {Daca, Przemyslaw and Henzinger, Thomas A. and Kretinsky, Jan and Petrov, Tatjana}, title = {{Linear Distances between Markov Chains}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {20:1--20:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.20}, URN = {urn:nbn:de:0030-drops-61829}, doi = {10.4230/LIPIcs.CONCUR.2016.20}, annote = {Keywords: probabilistic systems, verification, statistical model checking, temporal logic, behavioural equivalence} }

Document

**Published in:** LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Nested Weighted Limit-Average Automata of Bounded Width. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatterjee_et_al:LIPIcs.MFCS.2016.24, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Nested Weighted Limit-Average Automata of Bounded Width}}, booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)}, pages = {24:1--24:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-016-3}, ISSN = {1868-8969}, year = {2016}, volume = {58}, editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.24}, URN = {urn:nbn:de:0030-drops-64397}, doi = {10.4230/LIPIcs.MFCS.2016.24}, annote = {Keywords: weighted automata, nested weighted automata, complexity, mean-payoff} }

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**Published in:** LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)

Fault-tolerant distributed algorithms play an important role in many
critical/high-availability applications. These algorithms are notoriously difficult to implement correctly, due to asynchronous
communication and the occurrence of faults, such as the network
dropping messages or computers crashing. Nonetheless there is surprisingly little language and verification support to build
distributed systems based on fault-tolerant algorithms. In this
paper, we present some of the challenges that a designer has to
overcome to implement a fault-tolerant distributed system. Then we
review different models that have been proposed to reason about
distributed algorithms and sketch how such a model can form the basis
for a domain-specific programming language. Adopting a high-level
programming model can simplify the programmer's life and make the code
amenable to automated verification, while still compiling to
efficiently executable code. We conclude by summarizing the current
status of an ongoing language design and implementation project that
is based on this idea.

Cezara Dragoi, Thomas A. Henzinger, and Damien Zufferey. The Need for Language Support for Fault-Tolerant Distributed Systems. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 90-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{dragoi_et_al:LIPIcs.SNAPL.2015.90, author = {Dragoi, Cezara and Henzinger, Thomas A. and Zufferey, Damien}, title = {{The Need for Language Support for Fault-Tolerant Distributed Systems}}, booktitle = {1st Summit on Advances in Programming Languages (SNAPL 2015)}, pages = {90--102}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-80-4}, ISSN = {1868-8969}, year = {2015}, volume = {32}, editor = {Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.90}, URN = {urn:nbn:de:0030-drops-50192}, doi = {10.4230/LIPIcs.SNAPL.2015.90}, annote = {Keywords: Programming language, Fault-tolerant distributed algorithms, Automated verification} }

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**Published in:** LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity - a transducer is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation
using similarity functions. We show that K-robustness is undecidable even for deterministic transducers. We identify a class of functional transducers, which admits a polynomial time automata-theoretic decision procedure for K-robustness. This class includes Mealy machines and functional letter-to-letter transducers. We also study K-robustness of nondeterministic transducers. Since a nondeterministic transducer generates a set of output words for each input word, we quantify output perturbation using set-similarity functions. We show that K-robustness of nondeterministic transducers is undecidable, even for letter-to-letter transducers. We identify a class of set-similarity functions which admit decidable K-robustness of letter-to-letter transducers.

Thomas A. Henzinger, Jan Otop, and Roopsha Samanta. Lipschitz Robustness of Finite-state Transducers. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 431-443, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{henzinger_et_al:LIPIcs.FSTTCS.2014.431, author = {Henzinger, Thomas A. and Otop, Jan and Samanta, Roopsha}, title = {{Lipschitz Robustness of Finite-state Transducers}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {431--443}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.431}, URN = {urn:nbn:de:0030-drops-48614}, doi = {10.4230/LIPIcs.FSTTCS.2014.431}, annote = {Keywords: Robustness, Transducers, Weighted Automata} }

Document

**Published in:** LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Report on the Ackermann Award 2013.

Anuj Dawar, Thomas A. Henzinger, and Damian Niwiński. The Ackermann Award 2013. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{dawar_et_al:LIPIcs.CSL.2013.1, author = {Dawar, Anuj and Henzinger, Thomas A. and Niwi\'{n}ski, Damian}, title = {{The Ackermann Award 2013}}, booktitle = {Computer Science Logic 2013 (CSL 2013)}, pages = {1--4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-60-6}, ISSN = {1868-8969}, year = {2013}, volume = {23}, editor = {Ronchi Della Rocca, Simona}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.1}, URN = {urn:nbn:de:0030-drops-41837}, doi = {10.4230/LIPIcs.CSL.2013.1}, annote = {Keywords: Ackermann award} }

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**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential of approximate determinization. We define approximate determinization with respect to a distance function, and investigate this potential.
We show that sum automata cannot be determinized approximately with respect to any distance function. However, restricting to nonnegative weights allows for approximate determinization with respect to some distance functions.
Discounted-sum automata allow for approximate determinization, as the influence of a word's suffix is decaying. However, the naive approach, of unfolding the automaton computations up to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states. We prove matching lower bounds, showing exponential dependency on each of these three parameters.
Average and limit-average automata are shown to prohibit approximate determinization with respect to any distance function, and this is the case even for two weights, 0 and 1.

Udi Boker and Thomas A. Henzinger. Approximate Determinization of Quantitative Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 362-373, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{boker_et_al:LIPIcs.FSTTCS.2012.362, author = {Boker, Udi and Henzinger, Thomas A.}, title = {{Approximate Determinization of Quantitative Automata}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {362--373}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.362}, URN = {urn:nbn:de:0030-drops-38739}, doi = {10.4230/LIPIcs.FSTTCS.2012.362}, annote = {Keywords: Quantitative; Automata; Determinization; Approximation} }

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**Published in:** LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, which values a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by lambda^i, where the discount factor lambda is a fixed rational number greater than 1. Discounted summation is a common and useful measuring scheme, especially for infinite sequences, which reflects the assumption that earlier weights are more important than later weights. Determinizing automata is often essential, for example, in formal verification, where there are polynomial algorithms for comparing two deterministic NDAs, while the equivalence problem for NDAs is not known to be decidable.
Unfortunately, however, discounted-sum automata are, in general, not determinizable: it is currently known that for every rational discount factor 1 < lambda < 2, there is an NDA
with lambda (denoted lambda-NDA) that cannot be determinized.
We provide positive news, showing that every NDA with an integral factor is determinizable. We also complete the picture by proving that the integers characterize exactly the discount factors that guarantee determinizability: we show that for every non-integral rational factor lambda, there is a nondeterminizable lambda-NDA.
Finally, we prove that the class of NDAs with integral discount factors enjoys closure under the algebraic operations min, max, addition, and subtraction, which is not the case for general NDAs nor for deterministic NDAs. This shows that for integral discount factors, the class of NDAs forms an attractive specification formalism in quantitative formal verification. All our results hold equally for automata over finite words and for automata over infinite words.

Udi Boker and Thomas A. Henzinger. Determinizing Discounted-Sum Automata. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 82-96, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{boker_et_al:LIPIcs.CSL.2011.82, author = {Boker, Udi and Henzinger, Thomas A.}, title = {{Determinizing Discounted-Sum Automata}}, booktitle = {Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL}, pages = {82--96}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-32-3}, ISSN = {1868-8969}, year = {2011}, volume = {12}, editor = {Bezem, Marc}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.82}, URN = {urn:nbn:de:0030-drops-32243}, doi = {10.4230/LIPIcs.CSL.2011.82}, annote = {Keywords: Discounted-sum automata, determinization, quantitative verification} }

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**Published in:** LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources.
We prove the finite-memory determinacy of generalized energy games and show the inter-reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding
the existence of a winning strategy for the protagonist is NP-complete.

Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, and Jean-François Raskin. Generalized Mean-payoff and Energy Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 505-516, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chatterjee_et_al:LIPIcs.FSTTCS.2010.505, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A. and Raskin, Jean-Fran\c{c}ois}, title = {{Generalized Mean-payoff and Energy Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {505--516}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-23-1}, ISSN = {1868-8969}, year = {2010}, volume = {8}, editor = {Lodaya, Kamal and Mahajan, Meena}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.505}, URN = {urn:nbn:de:0030-drops-28484}, doi = {10.4230/LIPIcs.FSTTCS.2010.505}, annote = {Keywords: mean-payoff games, energy games, finite memory strategies, determinacy} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 6081, Software Verification: Infinite-State Model Checking and Static Program Analysis (2006)

Many software model checkers are based on predicate abstraction. If
the verification goal depends on pointer structures, the approach does
not work well, because it is difficult to find adequate predicate
abstractions for the heap. In contrast, shape analysis, which uses
graph-based heap abstractions, can provide a compact representation of
recursive data structures. We integrate shape analysis into the
software model checker BLAST. Because shape analysis is expensive, we
do not apply it globally. Instead, we ensure that, like predicates,
shape graphs are computed and stored locally, only where necessary for
proving the verification goal. To achieve this, we extend lazy
abstraction refinement, which so far has been used only for predicate
abstractions, to three-valued logical structures. This approach does
not only increase the precision of model checking, but it also
increases the efficiency of shape analysis. We implemented the
technique by extending BLAST with calls to TVLA.

Dirk Beyer, Thomas A. Henzinger, and Grégory Théoduloz. Lazy Shape Analysis. In Software Verification: Infinite-State Model Checking and Static Program Analysis. Dagstuhl Seminar Proceedings, Volume 6081, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{beyer_et_al:DagSemProc.06081.5, author = {Beyer, Dirk and Henzinger, Thomas A. and Th\'{e}oduloz, Gr\'{e}gory}, title = {{Lazy Shape Analysis}}, booktitle = {Software Verification: Infinite-State Model Checking and Static Program Analysis}, pages = {1--16}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {6081}, editor = {Parosh Aziz Abdulla and Ahmed Bouajjani and Markus M\"{u}ller-Olm}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06081.5}, URN = {urn:nbn:de:0030-drops-7284}, doi = {10.4230/DagSemProc.06081.5}, annote = {Keywords: Software model checking, Shape analysis, Counterexample-guided abstraction refinement, Interpolation, Predicate abstraction} }

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