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Decision procedures for inductive Boolean functions based on alternating automata

Abdelwaheb Ayari, David Basin, Felix Klaedtke
2003 Theoretical Computer Science  
We show how alternating automata provide decision procedures for the equality of inductively deÿned Boolean functions and present applications to reasoning about parameterized families of circuits.  ...  We provide complexity bounds for deciding the equality of function (or circuit) families and show how our decision procedures can be implemented using BDDs.  ...  Acknowledgements The authors thank Nils Klarlund and Aarti Gupta for helpful discussions. Appendix. Complete tree containment problem for ATAs  ... 
doi:10.1016/s0304-3975(02)00089-0 fatcat:uybkoixk5nh4vnae4py6dnrgni

Decision Procedures for Inductive Boolean Functions Based on Alternating Automata [chapter]

Abdelwaheb Ayari, David Basin, Felix Klaedtke
2000 Lecture Notes in Computer Science  
We show how alternating automata provide decision procedures for the equality of inductively deÿned Boolean functions and present applications to reasoning about parameterized families of circuits.  ...  We provide complexity bounds for deciding the equality of function (or circuit) families and show how our decision procedures can be implemented using BDDs.  ...  Acknowledgements The authors thank Nils Klarlund and Aarti Gupta for helpful discussions. Appendix. Complete tree containment problem for ATAs  ... 
doi:10.1007/10722167_16 fatcat:deteh3ggzff6dhye4h7ofkgi74

Page 2423 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
procedures for inductive Boolean functions based on alternating automata.  ...  This yields decision procedures for the equality of linearly inductive Boolean functions and exponentially inductive Boolean functions. Applying alternating automata has several advantages.  ... 

Integrating WS1S with PVS [chapter]

Sam Owre, Harald Rueß
2000 Lecture Notes in Computer Science  
It is based on new algorithms for minimizing finite-state automata using binary decision diagrams (BDDs) to represent transition functions in compressed form.  ...  Although this logic-automaton connection has been known for more than 40 years, it was only through the recent work at BRICS that it become possible to make effective use of automata-based decision procedures  ...  Møller for clarifying discussions about MONA internals, M. Sorea for comments on this paper, and S. Bensalem for providing interesting test cases.  ... 
doi:10.1007/10722167_42 fatcat:obik2mf2fvdvle5hetcievhhb4

Author index

2003 Theoretical Computer Science  
Klaedtke, Decision procedures for inductive Boolean functions based on alternating automata (1-3) 301-329 Basin, D., see A. Ayari (1-3) 301-329 Bouyer, P., see L.  ...  Cerny, On the non-termination of M DG -, A., Induction in the Timed Interval Calculus (1-3) 181-207 Winskel, G., see G.L. Cattani (1-3) 47-89  ... 
doi:10.1016/s0304-3975(03)00256-1 fatcat:uautyv2z55d45hwoj5aflam7ri

Mosel: A sound and efficient tool for M2L(Str) [chapter]

Peter Kelb, Tiziana Margaria, Michael Mendier, Claudia Gsottberger
1997 Lecture Notes in Computer Science  
MOSEL uses a hybrid representation of the automata: graphs with edges encoded as boolean functions and implemented via BDDs.  ...  Introduction MOSEL [6] is a new system for the analysis and verification in Monadic Second-Order Logic (M2L) based on model construction.  ... 
doi:10.1007/3-540-63166-6_45 fatcat:bzvs5jedxnc2tlb6msjvjuqoia

Bounded Model Construction for Monadic Second-Order Logics [chapter]

Abdelwaheb Ayari, David Basin
2000 Lecture Notes in Computer Science  
We present too preliminary tests using a SAT-based implementation of bounded model construction; for certain problem classes it can find counter-examples substantially faster than automata-based decision  ...  procedures.  ...  For generating length k counter-models, this yields a nonelementary improvement over the automata-based decision procedure for M2L-Str.  ... 
doi:10.1007/10722167_11 fatcat:z3twjz6u5jhl5em4pr42haum3e

The Impact of Alternation [article]

Radu Iosif, Xiao Xu
2017 arXiv   pre-print
In this paper we consider alternating automata over infinite alphabets, whose transition rules are formulae in a combined theory of booleans and some infinite data domain, that relate past and current  ...  Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware.  ...  Moreover, efficient exploration techniques based on antichains are shown to perform well for alternating automata over finite alphabets [5] .  ... 
arXiv:1705.05606v2 fatcat:cthqehganfdqhjvqydvtzuilli

Deciding Synchronous Kleene Algebra with Derivatives [chapter]

Sabine Broda, Sílvia Cavadas, Miguel Ferreira, Nelma Moreira
2015 Lecture Notes in Computer Science  
Using the notion of partial derivatives, we present a new decision procedure for equivalence between SKA terms.  ...  The results are extended for SKAT considering automata with transitions labeled by Boolean expressions instead of atoms.  ...  The implementation uses BDDs (binary decision diagrams) for dealing with boolean functions.  ... 
doi:10.1007/978-3-319-22360-5_5 fatcat:k4tgrfr3pzczvcwq2sdjqbamtq

SMT-based scenario verification for hybrid systems

Alessandro Cimatti, Sergio Mover, Stefano Tonetta
2012 Formal methods in system design  
HAN can be symbolically represented by means of SMT formulae, and analyzed by generalizing to the case of SMT the traditional model checking algorithms based on SAT.  ...  Hybrid automata networks (HAN) are a powerful formalism to model complex embedded systems.  ...  SMT solvers are tools which implement decision procedures for the SMT problem.  ... 
doi:10.1007/s10703-012-0158-0 fatcat:myexahgbszfytlzuphhky5naoy

SMT-Based Verification of Hybrid Systems

Alessandro Cimatti, Sergio Mover, Stefano Tonetta
2021 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
HAN can be symbolically represented by means of SMT formulae, and analyzed by generalizing to the case of SMT the traditional model checking algorithms based on SAT.  ...  Hybrid automata networks (HAN) are a powerful formalism to model complex embedded systems.  ...  SMT solvers are tools which implement decision procedures for the SMT problem.  ... 
doi:10.1609/aaai.v26i1.8442 fatcat:mjnhfx7s3ff2hgshobct5ed444

Verified decision procedures for MSO on words based on derivatives of regular expressions

Dmitriy Traytel, Tobias Nipkow
2013 Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13  
This paper presents a verified functional decision procedure for MSO formulas that is not based on automata but on regular expressions.  ...  Decision procedures for regular expression equivalence have been formalized before, usually based on Brzozowski derivatives.  ...  Acknowledgments We thank Alexander Krauss for inspiring discussions and Jasmin Christian Blanchette for numerous comments on the presentation.  ... 
doi:10.1145/2500365.2500612 dblp:conf/icfp/TraytelN13 fatcat:asrtidyayfamnf7tq36xjhh2ay

Verified decision procedures for MSO on words based on derivatives of regular expressions

DMITRIY TRAYTEL, TOBIAS NIPKOW
2015 Journal of functional programming  
., automata). This paper presents a verified functional decision procedure for MSO formulas that is not based on automata but on regular expressions.  ...  Decision procedures for regular expression equivalence have been formalized before, usually based on Brzozowski derivatives.  ...  Acknowledgments We thank Alexander Krauss for inspiring discussions and Jasmin Christian Blanchette for numerous comments on the presentation.  ... 
doi:10.1017/s0956796815000246 fatcat:rx442ooiebgdvkj3j2ceomnxum

Abstraction Refinement for Emptiness Checking of Alternating Data Automata [chapter]

Radu Iosif, Xiao Xu
2018 Lecture Notes in Computer Science  
In this paper we consider alternating automata over infinite alphabets, whose transition rules are formulae in a combined theory of Booleans and some infinite data domain, that relate past and current  ...  Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware.  ...  Moreover, efficient exploration techniques based on antichains are shown to perform well for alternating automata over finite alphabets [5] .  ... 
doi:10.1007/978-3-319-89963-3_6 fatcat:lbj4ojedgvbihnaiwixk3ui43m

A Theory of Restrictions for Logics and Automata [chapter]

Nils Klarlund
1999 Lecture Notes in Computer Science  
BDDs and their algorithms implement a decision procedure for Quantified Propositional Logic. BDDs are a kind of acyclic automata.  ...  procedure for string-oriented logic.  ...  And thanks to the referees for pointing out some errors in an earlier version.  ... 
doi:10.1007/3-540-48683-6_35 fatcat:llnt3ejb5bgfxfjek5hikwfrxa
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