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Model Checking Succinct and Parametric One-Counter Automata [chapter]

Stefan Göller, Christoph Haase, Joël Ouaknine, James Worrell
2010 Lecture Notes in Computer Science  
The aim of the present paper is to study the decidability and complexity of model checking for succinct and parametric one-counter automata.  ...  We were also influenced by the work of Demri and Gascon on model checking extensions of LTL over non-succinct, non-parametric one-counter automata [9], as well as the recent result of Göller and Lohrey  ...  We refer to such counter automata as succinct and parametric resp., the former being viewed as a subclass of the latter.  ... 
doi:10.1007/978-3-642-14162-1_48 fatcat:g4h6fbvqvfcrtpo5undtlaefi4

Advances in Parametric Real-Time Reasoning [chapter]

Daniel Bundala, Joël Ouaknine
2014 Lecture Notes in Computer Science  
By translating such problems as reachability questions in certain extensions of parametric one-counter machines, we show that, in the case of two parametric clocks (and arbitrarily many nonparametric clocks  ...  We study the decidability and complexity of the reachability problem in parametric timed automata.  ...  A similar construction was used in [5] to show that LTL model checking of parametric one-counter machines is NEXP-hard.  ... 
doi:10.1007/978-3-662-44522-8_11 fatcat:lpm5mihzdrfernwuon6xqgeaxi

Reachability in Succinct and Parametric One-Counter Automata [chapter]

Christoph Haase, Stephan Kreutzer, Joël Ouaknine, James Worrell
2009 Lecture Notes in Computer Science  
In this paper we consider one-counter automata with counter updates encoded in binary-which we refer to as the succinct encoding.  ...  We also consider parametric one-counter automata, in which counter updates be integer-valued parameters.  ...  The work that is closest to our own is that of Demri and Gascon on model checking extensions of LTL over one-counter automata [8] .  ... 
doi:10.1007/978-3-642-04081-8_25 fatcat:civltqmplfhx7jso7y7ozkn22i

Branching-Time Model Checking of Parametric One-Counter Automata [chapter]

Stefan Göller, Christoph Haase, Joël Ouaknine, James Worrell
2012 Lecture Notes in Computer Science  
We study the computational complexity of model checking EF logic and modal logic on parametric one-counter automata (POCA).  ...  Finally, we show that model checking EF logic on POCA without parameters is PSPACE-complete.  ...  Consequently, in this paper we restrict our attention to this class of counter automata, and in particular investigate model checking problems for succinct one-counter automata (SOCA) and parametric one-counter  ... 
doi:10.1007/978-3-642-28729-9_27 fatcat:hw74jyc6gjeyvbfl3xamh6iyi4

The Complexity of Flat Freeze LTL [article]

Benedikt Bollig, Karin Quaas, Arnaud Sangnier
2019 arXiv   pre-print
We consider the model-checking problem for freeze LTL on one-counter automata (OCA).  ...  In a previous work, Lechner et al. showed that model checking for flat freeze LTL on OCA with binary encoding of counter updates is decidable and in 2NEXPTIME.  ...  Introduction One-counter automata (OCA) are a simple yet fundamental computational model operating on a single counter that ranges over the non-negative integers.  ... 
arXiv:1609.06124v7 fatcat:zoc35zwzzng2fb5jsngx2mihly

Revisiting Reachability in Timed Automata [article]

Karin Quaas, Mahsa Shirmohammadi, James Worrell
2017 arXiv   pre-print
In this paper we give a new and simpler proof of this result, building on the well-known reachability analysis of timed automata involving difference bound matrices.  ...  Using this new proof, we give an exponential-space procedure for model checking the reachability fragment of the logic parametric TCTL. Finally we show that the latter problem is NEXPTIME-hard.  ...  This work was partially supported by the EPSRC through grants EP/M012298/1 and EP/M003795/1 and by the German Research Foundation (DFG), project QU 316/1-2.  ... 
arXiv:1702.03450v2 fatcat:jfqgafejabebzkz53uqueq5e4a

Revisiting Parameter Synthesis for One-Counter Automata [article]

Guillermo A. Pérez
2021 arXiv   pre-print
One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero.  ...  We study the (parameter) synthesis problem for one-counter automata with parameters.  ...  We also thank Michaël Cadilhac, Nathanaël Fijalkow, Philip Offtermatt, and Mikhail R. Starchak for useful feedback; Antonia Lechner and James Worrell for  ... 
arXiv:2005.01071v6 fatcat:35ej22hy5zakfkp7ujtbo65lgi

Expressive Equivalence and Succinctness of Parametrized Automata with Respect to Finite Memory Automata [chapter]

Tushant Jha, Walid Belkhir, Yannick Chevalier, Michael Rusinowitch
2016 Lecture Notes in Computer Science  
We prove that both classes have the same expressive power, while parametrized automata can be exponentially succinct in some cases.  ...  We compare parametrized automata, a class of automata recently introduced by the authors, against finite memory automata with non-deterministic assignment, an existing class of automata used to model services  ...  Considerable efforts have been devoted to extend finite automata to infinite alphabets: data automata [6] , finite memory automata [11] , usage automata [7] , fresh-variable automata [2] and parametrized  ... 
doi:10.1007/978-3-662-50539-7_12 fatcat:sfkf5bknyvbg3gpifbi62fkw4a

Succinct Determinisation of Counting Automata via Sphere Construction (Technical Report) [article]

Lukáš Holík, Ondřej Lengál, Olli Saarikivi, Lenka Turoňová, Margus Veanes, Tomáš Vojnar
2019 arXiv   pre-print
The algorithm avoids unfolding counters into control states, unlike the na\"ive approach, and thus produces much smaller deterministic automata.  ...  We propose an efficient algorithm for determinising counting automata (CAs), i.e., finite automata extended with bounded counters.  ...  In this paper, we call these automata counting automata (CAs). The main contribution of this paper is a novel succinct determinisation of CAs.  ... 
arXiv:1910.01996v1 fatcat:lvfp6kgw7fg75havdscjw7pxpu

Optimizing Automata Learning via Monads [article]

Gerco van Heerdt and Matteo Sammartino and Alexandra Silva
2019 arXiv   pre-print
The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects.  ...  The former perspective on monads allows us to develop a new algorithm and accompanying correctness proofs, building upon a general framework for automata learning based on category theory.  ...  [Chatterjee et al. 2008; Droste and Gastin 2005; Kuperberg 2014 ], to probabilistic model-checking [Baier et al. 2009] , to the verification of on-line algorithms [Aminof et al. 2010] .  ... 
arXiv:1704.08055v4 fatcat:4e4houzbefe63ioiel4vyxvuma

Survey on Parameterized Verification with Threshold Automata and the Byzantine Model Checker [article]

Igor Konnov and Marijana Lazić and Ilina Stoilkovska and Josef Widder
2022 arXiv   pre-print
In this article, we give an overview of the techniques implemented in Byzantine Model Checker (ByMC).  ...  Threshold guards are a basic primitive of many fault-tolerant algorithms that solve classical problems of distributed computing, such as reliable broadcast, two-phase commit, and consensus.  ...  This survey is based on the results of a long-lasting research agenda [JKS + 13a, KLVW17a, KLVW17b, LKWB17, BKLW19, SKWZ19, SKWZ21b].  ... 
arXiv:2011.14789v2 fatcat:zgx6tsgdnbehriqw2dor2dlbj4

A Symbolic Decision Procedure for Symbolic Alternating Finite Automata [article]

Loris D'Antoni, Zachary Kincaid, Fang Wang
2016 arXiv   pre-print
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets.  ...  Due to this succinctness, emptiness and equivalence checking are PSpace-hard. We introduce an algorithm for checking the equivalence of two s-AFAs based on bisimulation up to congruence.  ...  Conclusion We presented symbolic alternating finite automata, S-AFAs, a succinct and efficient automaton model for describing sets of finite sequences over large and potentially infinite alphabets.  ... 
arXiv:1610.01722v1 fatcat:3b3czuwwyncihguk54r2f2zouy

Reachability in two-parametric timed automata with one parameter is EXPSPACE-complete [article]

Stefan Göller, Mathieu Hilaire
2020 arXiv   pre-print
For the EXPSPACE upper bound, we give a careful exponential time reduction from PTA over two parametric clocks and one parameter to a slight subclass of parametric one-counter automata (POCA) over one  ...  This allows us to show a doubly-exponential upper bound on the value of the only parameter of a PTA over two parametric clocks and one parameter.  ...  We thank Benedikt Bollig and Karin Quaas for discussions and feedback.  ... 
arXiv:2011.07091v1 fatcat:a7iusfbpe5dvvdqgg2r3bdiucm

Deterministic Automata for Unordered Trees

Adrien Boiret, Vincent Hugot, Joachim Niehren, Ralf Treinen
2014 Electronic Proceedings in Theoretical Computer Science  
Depending on the choice of the order, we obtain different classes of automata, each of which has the same expressiveness as CMso.  ...  Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format.  ...  Preliminaries Automata on Ranked Ordered Trees We recall here the classical model of tree automata on ranked trees (cf. [4] for an introduction).  ... 
doi:10.4204/eptcs.161.17 fatcat:fpau4gbdurfpvc6cwehavcboty

Quantitative Automata under Probabilistic Semantics [article]

Krishnendu Chatterjee, Thomas A. Henzinger, Jan Otop
2019 arXiv   pre-print
Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties.  ...  For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent.  ...  On a single computation, i.e., between symbols $, A checks consistency of the transitions by checking two conditions: (C1) Boolean consistency, and (C2) counter consistency.  ... 
arXiv:1604.06764v3 fatcat:jbhgknsbtrfedlk5nfr323hryi
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