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Divide and Compose: SCC Refinement for Language Emptiness [chapter]

Chao Wang, Roderick Bloem, Gary D. Hachtel, Kavita Ravi, Fabio Somenzi
2001 Lecture Notes in Computer Science  
For language-emptiness checking, it quickly discards uninteresting parts of the state space; for the remaining states, it adapts the model checking computation to the strength of the SCCs at hand.  ...  We present a general framework for SCC refinement, which uses a compositional approach to generate and refine overapproximations.  ...  Specialized model checking algorithms for weak and especially terminal automata outperform the general language emptiness algorithm of Emerson can be used for terminal ones.  ... 
doi:10.1007/3-540-44685-0_31 fatcat:46borrqyw5ebrdpwohyh3ev6ui

Compositional SCC Analysis for Language Emptiness

Chao Wang, Roderick Bloem, Gary D. Hachtel, Kavita Ravi, Fabio Somenzi
2006 Formal methods in system design  
We propose a refinement approach to language emptiness, which is based on the enumeration and the successive refinements of SCCs on over-approximations of the exact system.  ...  It decomposes the state space disjunctively so that each state subset can be checked in isolation to decide language emptiness for the given system.  ...  The Divide and Compose (D'n'C) algorithm, whose entry function is GENERIC-REFINEMENT, takes as arguments a Büchi automaton A and a set L of over-approximations to A, When decomposing an SCC-closed set  ... 
doi:10.1007/s10703-006-4617-3 fatcat:lofbspsiqfhozk2ckhomuirmdq

Variations on parallel explicit emptiness checks for generalized Büchi automata

E. Renault, A. Duret-Lutz, F. Kordon, D. Poitrenaud
2016 International Journal on Software Tools for Technology Transfer (STTT)  
We present new parallel explicit emptiness checks for LTL model checking.  ...  Unlike existing parallel emptiness checks, these are based on a Strongly Connected Component (SCC) enumeration, support generalized Büchi acceptance, and require no synchronization points nor recomputing  ...  Among the 3268 formulas in our benchmark, 2406 generate automata with multiple SCC strengths (997 where the language of the product is empty, and 1409 where the language is non-empty).  ... 
doi:10.1007/s10009-016-0422-5 fatcat:qkqhvcsarbad5ktptj5lvk7ek4

Component-wise incremental LTL model checking

Vince Molnár, András Vörös, Dániel Darvas, Tamás Bartha, István Majzik
2016 Formal Aspects of Computing  
Complementing the search for SCCs, explicit techniques and component-wise abstractions are used to prove the absence of counterexamples.  ...  Efficient symbolic and explicit-state model checking approaches have been developed for the verification of linear time temporal logic (LTL) properties.  ...  The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.  ... 
doi:10.1007/s00165-015-0347-x fatcat:atvkwn3rgjb73luyyvxnttn7cq

Emptiness and Universality Problems in Timed Automata with Positive Frequency [chapter]

Nathalie Bertrand, Patricia Bouyer, Thomas Brihaye, Amélie Stainer
2011 Lecture Notes in Computer Science  
We study various properties of timed languages accepted with positive frequency, and in particular the emptiness and universality problems.  ...  The languages of infinite timed words accepted by timed automata are traditionally defined using Büchi-like conditions.  ...  Emptiness and Universality Problems The emptiness problem.  ... 
doi:10.1007/978-3-642-22012-8_19 fatcat:r2ao6negrnex5jnk7bwcwp2cr4

A propositional dense time logic [chapter]

Mohsin Ahmed, G. Venkatesh
1993 Lecture Notes in Computer Science  
Ordinal trees can be easily embedded as a temporal data structure in a conventional logic programming language and thus provide a framework for temporal logic programming.  ...  Ordinal tree models though based on dense points, represent interval based information which maybe refined to any finite level.  ...  An empty node is considered open. If ~ node contains both A and ~A (or ~'), then it is obviously unsatisfiable and therefore closed.  ... 
doi:10.1007/3-540-56610-4_91 fatcat:wcfc4csw5jetlex3lq6vafb5q4

Locality and Centrality: The Variety ZG [article]

Antoine Amarilli, Charles Paperman
2021 arXiv   pre-print
finite unions of disjoint shuffles of singleton languages and regular commutative languages.  ...  In the process, we obtain the characterization ZG = MNil \vee Com, and also characterize the ZG languages, i.e., the languages whose syntactic monoid is in ZG: they are precisely the languages that are  ...  For any alphabet Σ, for any n > 0, for any m > 0, if m is a multiple of n then the m-congruence refines the n-congruence.  ... 
arXiv:2102.07724v2 fatcat:24zdlui5njctplzdvdar33yqym

Page 556 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
Hachtel, Kavita Ravi and Fabio Somenzi, Divide and compose: SCC refinement for language emptiness (456-471); Marie Duflot, Laurent Fribourg and Ulf Nilsson, Unavoidable configurations of parameterized  ...  232); Jaco Geldenhuys and Antti Val- mari, Techniques for smaller intermediary BDDs (233-247); Patri- cia Bouyer, Antoine Petit and Denis Thérien, An algebraic charac- terization of data and timed languages  ... 

Efficient Model Checking of Safety Properties [chapter]

Timo Latvala
2003 Lecture Notes in Computer Science  
Our first contribution is a theorem relating abstraction for Coloured Petri nets as defined by Lakos [36] and preservation of safety properties.  ...  Minor contributions include new proofs for some old complexity results regarding LTL and safety properties. The implementation of the translation algorithm is also experimentally evaluated.  ...  ACKNOWLEDGEMENTS The author thanks Keijo Heljanko for fruitful discussions and comments on the paper.  ... 
doi:10.1007/3-540-44829-2_5 fatcat:zlkczcjjdfeijoekb66ohrtpe4

Breaking ties in collective decision-making

Daniela Bubboloni, Michele Gori
2020 Decisions in Economics and Finance  
We also clear when it is possible to obtain, for those resolute refinements, the reversal symmetry (immunity to the reversal bias).  ...  The theory we develop turns out to be useful in many common applicative contexts and allows to explicitly construct those refinements.  ...  Consider, for instance, a faculty committee composed by full and associate professors which is going to select some applicants for an academic position.  ... 
doi:10.1007/s10203-020-00294-8 fatcat:2xrppbi2evg2dcsirvzd3v5ewe

Scalable Multi-core Model Checking Fairness Enhanced Systems [chapter]

Yang Liu, Jun Sun, Jin Song Dong
2009 Lecture Notes in Computer Science  
We enhance our PAT model checker with the technique and show its usability via the automated verification of several real-life systems.  ...  Experimental results show that our approach is scalable, especially when a system search space contains many SCCs.  ...  There are two SCCs, namely scc1 which is composed of state 1 only and scc2 which is composed of state 0, 2 and 3.  ... 
doi:10.1007/978-3-642-10373-5_22 fatcat:jqpgqhqxk5bi3b6xi4gmohzl6a

An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties [article]

Yong Li and Wanwei Liu and Andrea Turrini and Ernst Moritz Hahn and Lijun Zhang
2016 arXiv   pre-print
The algorithm works also for interval Markov chains. The complexity is linear in the size of the Markov chain, and exponential in the size of the formula.  ...  The PLTL formula is translated to an almost fully partitioned B\"uchi automaton which is then composed with the parametric Markov chain.  ...  Intuitively, in the product G composed by an almost reverse deterministic automaton A and a PMC M, the complete SCCs must be the SCCs whose preceded SCCs should not have the same projections.  ... 
arXiv:1605.04400v1 fatcat:pwquduxrvvdifekzku4ajj3dlq

Saturation-Based Incremental LTL Model Checking with Inductive Proofs [chapter]

Vince Molnár, Dániel Darvas, András Vörös, Tamás Bartha
2015 Lecture Notes in Computer Science  
Efficient symbolic and explicit model checking approaches have been developed for the verification of linear time temporal properties.  ...  In addition, our solution works on-the-fly during state space traversal and exploits the decomposition of the model as an abstraction to inductively prove the absence of SCCs with cheap explicit runs on  ...  Checking these properties is usually reduced to finding strongly connected components (SCCs) by checking language emptiness of the synchronous product of two Büchi automata: one characterizing the possible  ... 
doi:10.1007/978-3-662-46681-0_58 fatcat:yqbmwk7bizfczpzvqf3vjwj7ii

Test Generation Derived from Model-Checking [chapter]

Thierry Jéron, Pierre Morel
1999 Lecture Notes in Computer Science  
Model-checking and testing are different activities, at least conceptually.  ...  Nevertheless, there are also similarities in models and algorithms.  ...  A specification is given in a formal description language (e.g.  ... 
doi:10.1007/3-540-48683-6_12 fatcat:57wjq2dlgfazfjsh43irtje2wy

Incremental qualitative temporal reasoning: Algorithms for the Point Algebra and the ORD-Horn class

Alfonso Gerevini
2005 Artificial Intelligence  
The reasoning algorithms for PA and the tractable fragments of IA, such as Nebel and Bürckert's maximal tractable class of relations (ORD-Horn), have originally been designed for "static" reasoning.  ...  The Point Algebra (PA) and the Interval Algebra (IA) are two well-known frameworks for qualitative temporal reasoning.  ...  As a final remark, we observe that FEASIBLE could be improved by initializing C to SCC * [w, z, r ] instead of the empty set.  ... 
doi:10.1016/j.artint.2005.04.005 fatcat:52sydbdppre7tgqccawxo4emdi
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