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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.  ...  Boolean operations over s-AFAs have linear complexity, which is in sharp contrast with the quadratic cost of intersection and union for non-alternating symbolic automata.  ...  Symbolic alternating finite automata This section gives a formal description of symbolic alternating finite automata (S-AFA).  ... 
arXiv:1610.01722v1 fatcat:3b3czuwwyncihguk54r2f2zouy

Page 1778 of Mathematical Reviews Vol. 41, Issue 6 [page]

1971 Mathematical Reviews  
L. 9668 The decision problems of definite stochastic automata. SIAM J. Control 8 (1970), 124-134. This paper presents a time-saving decision procedure for the definiteness of stochastic automata.  ...  A k-definite stochastic automaton is defined as a finite stochastic automaton in which the state probability distribution depends only on the last & input symbols for some definite integer & or, alternatively  ... 

Nested Antichains for WS1S [article]

Tomas Fiedor, Lukas Holik, Ondrej Lengal, Tomas Vojnar
2015 arXiv   pre-print
The way in which the standard decision procedure processes quantifiers involves determinization, with its worst case exponential complexity, for every quantifier alternation in the prefix of a formula.  ...  Our approach is applicable within the state-of-the-art automata-based WS1S decision procedure implemented, e.g. in MONA.  ...  In Sections 3 and 4, we introduce finite word automata and describe the classical decision procedure for WS1S based on finite word automata.  ... 
arXiv:1501.03849v1 fatcat:mp6d6kfijzazxfanakfjz3wjhi

Verification of Infinite-State Systems by Combining Abstraction and Reachability Analysis [chapter]

Parosh Aziz Abdulla, Aurore Annichini, Saddek Bensalem, Ahmed Bouajjani, Peter Habermehl, Yassine Lakhnech
1999 Lecture Notes in Computer Science  
We develop a general methodology for analyzing such systems based on combining automatic generation of abstract models (not necessarily finite-state) with symbolic reachability analysis.  ...  We propose a realization of this approach in a framework which extends PVS with automatic invariant checking strategies, automatic procedures for generating abstract models, as well as automatabased decision  ...  Amore [24] (which provides a library of procedures on finite-state automata), and an automatic procedure for computing abstract models using automata-based decision procedures.  ... 
doi:10.1007/3-540-48683-6_15 fatcat:7i7pjhprhnaf5bkiqyyzcvmw34

Alternating Automata Modulo First Order Theories [chapter]

Radu Iosif, Xiao Xu
2019 Lecture Notes in Computer Science  
This provides a method for checking inclusion of timed and finite-memory register automata, and emptiness of quantified predicate automata, previously used in the verification of parameterized concurrent  ...  We introduce first-order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first-order formulae, with states and internal variables  ...  Since even such simple classes of alternating automata have no general decision procedure for emptiness, we use an abstraction-refinement semi-algorithm based on lazy annotation [20, 21] .  ... 
doi:10.1007/978-3-030-25543-5_3 fatcat:bidjq27ybnhzdcllzjthwvygea

A note on realtime one-way synchronized alternating one-counter automata

Juraj Hromkovič, Katsushi Inoue
1993 Theoretical Computer Science  
A note on realtime one-\\ay synchronized alternating one-counter automata.  ...  alternating finite automata do the same [6] .  ...  We. finall). show that realtime synchronized alternating finite automata recognize esactlq regular sets. i.e.. that one counter is more powerful than no counter for realtime sgnchronizrd alternating automata  ... 
doi:10.1016/0304-3975(93)90203-6 fatcat:4wvizewufbg3jfunhpagihhxki

Lazy Automata Techniques for WS1S [article]

Tomáš Fiedor, Lukáš Holík, Petr Janků, Ondřej Lengál, Tomáš Vojnar
2017 arXiv   pre-print
We present a new decision procedure for the logic WS1S.  ...  The pruning is done by a generalization of two techniques used in antichain-based language inclusion and universality checking of finite automata: subsumption and early termination.  ...  We thank the anonymous reviewers for their helpful comments on how to improve the presentation in this paper.  ... 
arXiv:1701.06282v2 fatcat:k5w45yi5znc5rh6fq5cqwvdwy4

Lazy Automata Techniques for WS1S [chapter]

Tomáš Fiedor, Lukáš Holík, Petr Janků, Ondřej Lengál, Tomáš Vojnar
2017 Lecture Notes in Computer Science  
We present a new decision procedure for the logic WS1S.  ...  The pruning is done by a generalization of two techniques used in antichain-based language inclusion and universality checking of finite automata: subsumption and early termination.  ...  We thank the anonymous reviewers for their helpful comments on how to improve the presentation in this paper.  ... 
doi:10.1007/978-3-662-54577-5_24 fatcat:nyebae6pejhhhokccc2pipxp7m

Symbolic tree automata

Margus Veanes, Nikolaj Bjørner
2015 Information Processing Letters  
We introduce symbolic tree automata as a generalization of finite tree automata with a parametric alphabet over any given background theory.  ...  This generalizes the corresponding classical properties known for finite tree automata.  ...  The notion of an alternating symbolic tree automaton is also introduced in [10] . Alternating STAs arise naturally as domain automata of nonlinear symbolic tree transducers.  ... 
doi:10.1016/j.ipl.2014.11.005 fatcat:5ferufzh5ngmnergriuesqsbqe

Alternating, private alternating, and quantum alternating realtime automata [article]

Gökalp Demirci and Mika Hirvensalo and Klaus Reinhardt and A. C. Cem Say and Abuzer Yakaryılmaz
2019 arXiv   pre-print
Regarding quantum finite automata (QFAs), we show that the emptiness problem is undecidable both for universal QFAs on general alphabets, and for alternating QFAs with two alternations on unary alphabets  ...  Then, we present two equivalent definitions of realtime private alternating finite automata (PAFAs). We show that the emptiness problem is undecidable for PAFAs.  ...  Acknowledgements We thank the anonymous reviewers for their helpful comments.  ... 
arXiv:1407.0334v4 fatcat:7ex2kzyb35atdicov25gejjmvm

Bounded model checking of infinite state systems

Tobias Schuele, Klaus Schneider
2006 Formal methods in system design  
Bounded model checking (BMC) is an attractive alternative to symbolic model checking, since it often allows a more efficient verification.  ...  The idea of BMC is to reduce the model checking problem to a satisfiability problem of the underlying base logic, so that sophisticated decision procedures can be utilized to check the resulting formula  ...  Acknowledgments We thank the reviewers for their detailed and valuable comments that helped us to substantially improve this paper.  ... 
doi:10.1007/s10703-006-0019-9 fatcat:ahphd3hr5zdhfaor3ak6mgkpyy

An Efficient Finite Tree Automata Library [article]

Ondřej Lengál
2012 arXiv   pre-print
Thus the aim of this Master's Thesis is to provide such a library. The present paper first describes the theoretical background of finite tree automata and regular tree languages.  ...  However, currently there is no tree automata library implementation that would provide an efficient and flexible support for such methods.  ...  Independently of MONA, Glenn and Gasarch [16] also implemented an automaton-based decision procedure for WS1S.  ... 
arXiv:1204.3240v1 fatcat:mzkxqmjemjeplnoy2kmizjwzvi

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

Damien Pous
2015 Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '15  
We first propose algorithms for checking language equivalence of finite automata over a large alphabet.  ...  We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD).  ...  A similar study for the symbolic counterpart we propose here seems out of reach for now.  ... 
doi:10.1145/2676726.2677007 dblp:conf/popl/Pous15 fatcat:j2mvfbjfazchfisc35wwpvmodq

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

Damien Pous
2015 SIGPLAN notices  
We first propose algorithms for checking language equivalence of finite automata over a large alphabet.  ...  We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD).  ...  A similar study for the symbolic counterpart we propose here seems out of reach for now.  ... 
doi:10.1145/2775051.2677007 fatcat:l4tyh2tryzdu5cbgsenhs7k7am

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests [article]

Damien Pous
2014 arXiv   pre-print
We first propose algorithms for checking language equivalence of finite automata over a large alphabet.  ...  We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD).  ...  By symbolic automata, we mean finite automata whose transition function is represented using a compact data-structure, typically binary decision diagrams (BDDs) [9, 10] , allowing the explore the automata  ... 
arXiv:1407.3213v1 fatcat:sqdvpp2jvndpdjbslpphql2nza
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