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DOI: 10.4230/LIPIcs.STACS.2025.20

On Cascades of Reset Automata

Authors: Roberto Borelli, Luca Geatti, Marco Montali, and Angelo Montanari

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract

The Krohn-Rhodes decomposition theorem is a pivotal result in automata theory. It introduces the concept of cascade product, where two semiautomata, that is, automata devoid of initial and final states, are combined in a feed-forward fashion. The theorem states that any semiautomaton can be decomposed into a sequence of permutation-reset semiautomata. For the counter-free case, this decomposition consists entirely of reset components with two states each. This decomposition has significantly impacted recent research in various areas of computer science, including the identification of a class of transformer encoders equivalent to star-free languages and the conversion of Linear Temporal Logic formulas into past-only expressions (pastification). The paper revisits the cascade product in the context of reset automata, thus considering each component of the cascade as a language acceptor. First, we give regular expression counterparts of cascades of reset automata. We then establish several expressiveness results, identifying hierarchies of languages based on the restriction of the height (number of components) of the cascade or of the number of states in each level. We also show that any cascade of reset automata can be transformed, with a quadratic increase in height, into a cascade that only includes two-state components. Finally, we show that some fundamental operations on cascades, like intersection, union, negation, and concatenation with a symbol to the left, can be directly and efficiently computed by adding a two-state component.

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Roberto Borelli, Luca Geatti, Marco Montali, and Angelo Montanari. On Cascades of Reset Automata. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{borelli_et_al:LIPIcs.STACS.2025.20,
  author =	{Borelli, Roberto and Geatti, Luca and Montali, Marco and Montanari, Angelo},
  title =	{{On Cascades of Reset Automata}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.20},
  URN =		{urn:nbn:de:0030-drops-228453},
  doi =		{10.4230/LIPIcs.STACS.2025.20},
  annote =	{Keywords: Automata, Cascade products, Regular expressions, Krohn-Rhodes theory}
}

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DOI: 10.4230/DagSemProc.07122.15

Expressing and Verifying Business Contracts with Abductive

Authors: Marco Alberti, Federico Chesani, Marco Gavanelli, Evelina Lamma, Paola Mello, Marco Montali, and Paolo Torroni

Published in: Dagstuhl Seminar Proceedings, Volume 7122, Normative Multi-agent Systems (2007)

Abstract

In this article, we propose to adopt the SCIFF abductive logic language to specify business contracts, and show how its proof procedures are useful to verify contract execution and fulfilment. SCIFF is a declarative language based on abductive logic programming, which accommodates forward rules, predicate definitions, and constraints over finite domain variables. Its declarative semantics is abductive, and can be related to that of deontic operators; its operational specification is the sound and complete SCIFF proof procedure, defined as a set of transition rules, which has been implemented and integrated into a reasoning and verification tool. A variation of the SCIFF proof-procedure (g-SCIFF) can be used for static verification of contract properties. We demonstrate the use of the SCIFF language for business contract specification and verification, in a concrete scenario. In order to accommodate integration of SCIFF with architectures for business contract, we also propose an encoding of SCIFF contract rules in RuleML.

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Marco Alberti, Federico Chesani, Marco Gavanelli, Evelina Lamma, Paola Mello, Marco Montali, and Paolo Torroni. Expressing and Verifying Business Contracts with Abductive. In Normative Multi-agent Systems. Dagstuhl Seminar Proceedings, Volume 7122, pp. 1-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{alberti_et_al:DagSemProc.07122.15,
  author =	{Alberti, Marco and Chesani, Federico and Gavanelli, Marco and Lamma, Evelina and Mello, Paola and Montali, Marco and Torroni, Paolo},
  title =	{{Expressing and Verifying Business Contracts with Abductive}},
  booktitle =	{Normative Multi-agent Systems},
  pages =	{1--29},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7122},
  editor =	{Guido Boella and Leon van der Torre and Harko Verhagen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07122.15},
  URN =		{urn:nbn:de:0030-drops-9017},
  doi =		{10.4230/DagSemProc.07122.15},
  annote =	{Keywords: Contracts, Verification, Abduction}
}

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Documents authored by Montali, Marco

On Cascades of Reset Automata

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Expressing and Verifying Business Contracts with Abductive

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