4 Search Results for "Becker, Martin"


Document
Sorting Finite Automata via Partition Refinement

Authors: Ruben Becker, Manuel Cáceres, Davide Cenzato, Sung-Hwan Kim, Bojana Kodric, Francisco Olivares, and Nicola Prezza

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Wheeler nondeterministic finite automata (WNFAs) were introduced in (Gagie et al., TCS 2017) as a powerful generalization of prefix sorting from strings to labeled graphs. WNFAs admit optimal solutions to classic hard problems on labeled graphs and languages such as compression and regular expression matching. The problem of deciding whether a given NFA is Wheeler is known to be NP-complete (Gibney and Thankachan, ESA 2019). Recently, however, Alanko et al. (Information and Computation 2021) showed how to side-step this complexity by switching to preorders: letting Q be the set of states and δ the set of transitions, they provided a O(|δ|⋅|Q|²)-time algorithm computing a totally-ordered partition (i.e. equivalence relation) of the WNFA’s states such that (1) equivalent states recognize the same regular language, and (2) the order of (the classes of) non-equivalent states is consistent with any Wheeler order, when one exists. As a result, the output is a preorder of the states as useful for pattern matching as standard Wheeler orders. Further extensions of this line of work (Cotumaccio et al., SODA 2021 and DCC 2022) generalized these concepts to arbitrary NFAs by introducing co-lex partial preorders: in general, any NFA admits a partial preorder of its states reflecting the co-lexicographic order of their accepted strings; the smaller the width of such preorder is, the faster regular expression matching queries can be performed. To date, the fastest algorithm for computing the smallest-width partial preorder on NFAs runs in O(|δ|² + |Q|^{5/2}) time (Cotumaccio, DCC 2022), while on DFAs the same task can be accomplished in O(min(|Q|²log|Q|, |δ|⋅|Q|)) time (Kim et al., CPM 2023). In this paper, we provide much more efficient solutions to the co-lex order computation problem. Our results are achieved by extending a classic algorithm for the relational coarsest partition refinement problem of Paige and Tarjan to work with ordered partitions. More specifically, we provide a O(|δ|log|Q|)-time algorithm computing a co-lex total preorder when the input is a Wheeler NFA, and an algorithm with the same time complexity computing the smallest-width co-lex partial order of any DFA. In addition, we present implementations of our algorithms and show that they are very efficient also in practice.

Cite as

Ruben Becker, Manuel Cáceres, Davide Cenzato, Sung-Hwan Kim, Bojana Kodric, Francisco Olivares, and Nicola Prezza. Sorting Finite Automata via Partition Refinement. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{becker_et_al:LIPIcs.ESA.2023.15,
  author =	{Becker, Ruben and C\'{a}ceres, Manuel and Cenzato, Davide and Kim, Sung-Hwan and Kodric, Bojana and Olivares, Francisco and Prezza, Nicola},
  title =	{{Sorting Finite Automata via Partition Refinement}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.15},
  URN =		{urn:nbn:de:0030-drops-186684},
  doi =		{10.4230/LIPIcs.ESA.2023.15},
  annote =	{Keywords: Wheeler automata, prefix sorting, pattern matching, graph compression, sorting, partition refinement}
}
Document
Solving hard instances in QF-BV combining Boolean reasoning with computer algebra

Authors: Markus Wedler, Evgeny Pavlenko, Alexander Dreyer, Frank Seelisch, Dominik Stoffel, Gert-Martin Greuel, and Wolfgang Kunz

Published in: Dagstuhl Seminar Proceedings, Volume 9461, Algorithms and Applications for Next Generation SAT Solvers (2010)


Abstract
This paper describes our new satisfyability (SAT) modulo theory (SMT) solver STABLE for the quantifier-free logic over fixed size bit vectors. Our main application domain is formal verification of system-on-chip (SoC) modules designed for complex computational tasks, for example, in signal processing applications. Ensuring proper functional behavior for such modules, including arithmetic correctness of the data paths, is considered a very difficult problem. We show how methods from computer algebra can be integrated into an SMT solver such that instances can be handled where the arithmetic problem parts are specified mixing various levels of abstraction from the plain gate level for small highly optimized components up to the pure word level used in high-level specifications. If the arithmetic problem parts include multiplications such mixed problem descriptions quickly drive current SMT solvers towards their capacity limits. High performance data paths are often designed at a level of abstraction that we call the arithmetic bit level (ABL). We show how ABL information, if available in an SMT instance, can be used to transform the decision problem into an equivalent set of variety subset problems. These problems can be solved efficiently with techniques from computer algebra based on Gröbner basis theory over finite rings Z/2^n . Sometimes, instances contain problem parts at a level below the ABL using gate-level operations. These problem parts, e.g., originate from custom-designed arithmetic components that are highly optimized using the gate-level constructs of a hardware description language (HDL). For such cases we integrate a local ABL extraction technique based on local Reed-Muller forms.

Cite as

Markus Wedler, Evgeny Pavlenko, Alexander Dreyer, Frank Seelisch, Dominik Stoffel, Gert-Martin Greuel, and Wolfgang Kunz. Solving hard instances in QF-BV combining Boolean reasoning with computer algebra. In Algorithms and Applications for Next Generation SAT Solvers. Dagstuhl Seminar Proceedings, Volume 9461, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{wedler_et_al:DagSemProc.09461.4,
  author =	{Wedler, Markus and Pavlenko, Evgeny and Dreyer, Alexander and Seelisch, Frank and Stoffel, Dominik and Greuel, Gert-Martin and Kunz, Wolfgang},
  title =	{{Solving hard instances in QF-BV combining Boolean reasoning with computer algebra}},
  booktitle =	{Algorithms and Applications for Next Generation SAT Solvers},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9461},
  editor =	{Bernd Becker and Valeria Bertacoo and Rolf Drechsler and Masahiro Fujita},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09461.4},
  URN =		{urn:nbn:de:0030-drops-25096},
  doi =		{10.4230/DagSemProc.09461.4},
  annote =	{Keywords: SAT modulo Theory, Quantifier Free logic over fixed sized bitvectors; Computer Algebra}
}
Document
Towards Model Validation and Verification with SAT Techniques

Authors: Martin Gogolla

Published in: Dagstuhl Seminar Proceedings, Volume 9461, Algorithms and Applications for Next Generation SAT Solvers (2010)


Abstract
After sketching how system development and the UML (Unified Modeling Language) and the OCL (Object Constraint Language) are related, validation and verification with the tool USE (UML-based Specification Environment) is demonstrated. As a more efficient alternative for verification tasks, two approaches using SAT-based techniques are put forward: First, a direct encoding of UML and OCL with Boolean variables and propositional formulas, and second, an encoding employing an intermediate, higher-level language (KODKOD, stongly connected to ALLOY). A number of further, presently not realized verification and validation tasks and the transformation of higher-level modeling concepts into simple UML/OCL models, which are checkable with SAT-based techniques, are shortly discussed. Finally, the potential of SAT-based techniques for model development is again emphasized.

Cite as

Martin Gogolla. Towards Model Validation and Verification with SAT Techniques. In Algorithms and Applications for Next Generation SAT Solvers. Dagstuhl Seminar Proceedings, Volume 9461, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{gogolla:DagSemProc.09461.6,
  author =	{Gogolla, Martin},
  title =	{{Towards Model Validation and Verification with SAT Techniques}},
  booktitle =	{Algorithms and Applications for Next Generation SAT Solvers},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9461},
  editor =	{Bernd Becker and Valeria Bertacoo and Rolf Drechsler and Masahiro Fujita},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09461.6},
  URN =		{urn:nbn:de:0030-drops-25078},
  doi =		{10.4230/DagSemProc.09461.6},
  annote =	{Keywords: UML, OCL, Invariant, Pre- and postcondition, Model validation, Model verification}
}
Document
Software Architecture Trends and Promising Technology for Ambient Assisted Living Systems

Authors: Martin Becker

Published in: Dagstuhl Seminar Proceedings, Volume 7462, Assisted Living Systems - Models, Architectures and Engineering Approaches (2008)


Abstract
Driven by the ongoing demographical, structural, and social changes in all modern, industrialized countries, there is a huge interest in IT-based equipment and services these days that enable independent living of people with specific needs. Despite of promising concepts, approaches and technology, those systems are still rather a vision than reality. In order to pave the way towards a common understanding of the problem and overall software solution approaches, this paper (i) characterizes the Ambient Assisted Living domain, (ii) briefly presents relevant software architecture trends, esp. applicable styles and patterns and (iii) discusses promising software technology already available to solve the problems.

Cite as

Martin Becker. Software Architecture Trends and Promising Technology for Ambient Assisted Living Systems. In Assisted Living Systems - Models, Architectures and Engineering Approaches. Dagstuhl Seminar Proceedings, Volume 7462, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{becker:DagSemProc.07462.23,
  author =	{Becker, Martin},
  title =	{{Software Architecture Trends and Promising Technology for Ambient Assisted Living Systems}},
  booktitle =	{Assisted Living Systems - Models, Architectures and Engineering Approaches},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7462},
  editor =	{Arthur I. Karshmer and J\"{u}rgen Nehmer and Hartmut Raffler and Gerhard Tr\"{o}ster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07462.23},
  URN =		{urn:nbn:de:0030-drops-14551},
  doi =		{10.4230/DagSemProc.07462.23},
  annote =	{Keywords: Ambient Assisted Living, Software Architecture, Technology, Middleware}
}
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