On store languages and applications

Abstract The store language of a machine of some arbitrary type is the set of all store configurations (state plus store contents but not input) that can appear in an accepting computation. New algorithms and characterizations of store languages are obtained, such as the result that any nondeterministic pushdown automaton augmented with reversal-bounded counters, where the pushdown can “flip” its contents a bounded number of times, can be accepted by a machine with only reversal-bounded counters. Connections are made between store languages and several model checking and reachability problems, such as accepting the set of all predecessor and successor configurations of a machine from a given (regular) set of configurations. For a variety of different machine models often containing multiple parallel data stores, these sets can be accepted with a machine model that is simpler than the original model itself. Store languages are key to showing these properties.

[1]  Alain Finkel,et al.  Bounded Parikh Automata , 2011, WORDS.

[2]  Michaël Cadilhac,et al.  On the Expressiveness of Parikh Automata and Related Models , 2011, NCMA.

[3]  Oscar H. Ibarra,et al.  On the Density of Languages Accepted by Turing Machines and Other Machine Models , 2018, J. Autom. Lang. Comb..

[4]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[5]  Richard Stanley.  Review: Sheila A. Greibach, A Note on Pushdown Store Automata and Regular Systems , 1968 .

[6]  C. Jung.  THE COLLECTED WORKS OF , 2014 .

[7]  Eitan M. Gurari,et al.  The Complexity of Decision Problems for Finite-Turn Multicounter Machines , 1981, J. Comput. Syst. Sci..

[8]  Anthony Widjaja Lin,et al.  Model Checking Recursive Programs with Numeric Data Types , 2011, CAV.

[9]  Tayssir Touili,et al.  Regular Symbolic Analysis of Dynamic Networks of Pushdown Systems , 2005, CONCUR.

[10]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[11]  Mohamed Faouzi Atig,et al.  Global Model Checking of Ordered Multi-Pushdown Systems , 2010, FSTTCS.

[12]  Tero Harju,et al.  Some Decision Problems Concerning Semilinearity and Commutation , 2002, J. Comput. Syst. Sci..

[13]  Anthony Widjaja Lin,et al.  Synchronisation- and Reversal-Bounded Analysis of Multithreaded Programs with Counters , 2012, CAV.

[14]  Oscar H. Ibarra,et al.  On Store Languages of Language Acceptors , 2017, Theor. Comput. Sci..

[15]  Martin Kutrib,et al.  Flip-Pushdown Automata: Nondeterminism Is Better than Determinism , 2003, Developments in Language Theory.

[16]  Nivat G. Päun,et al.  Handbook of Formal Languages , 2013, Springer Berlin Heidelberg.

[17]  Oscar H. Ibarra,et al.  On Bounded Semilinear Languages, Counter Machines, and Finite-Index ET0L , 2016, CIAA.

[18]  Oscar H. Ibarra,et al.  Semilinearity of Families of Languages , 2018, CIAA.

[19]  J. Richard Biichi.  The Collected Works of J. Richard Büchi , 1990, Springer New York.

[20]  Dirk Siefkes,et al.  The collected works of J. Richard Büchi , 1989 .

[21]  Luca Breveglieri,et al.  Multi-Push-Down Languages and Grammars , 1996, Int. J. Found. Comput. Sci..

[22]  Grzegorz Rozenberg,et al.  Handbook of Formal Languages , 1997, Springer Berlin Heidelberg.

[23]  Alain Finkel,et al.  Decidability of Reachability Problems for Classes of Two Counters Automata , 2000, STACS.

[24]  Anthony Widjaja Lin,et al.  Decidable Models of Integer-Manipulating Programs with Recursive Parallelism , 2016, RP.

[25]  Michael A. Arbib,et al.  An Introduction to Formal Language Theory , 1988, Texts and Monographs in Computer Science.

[26]  Oscar H. Ibarra,et al.  Reachability Analysis for Some Models of Infinite-State Transition Systems , 2000, CONCUR.

[27]  Benedikt Bollig,et al.  Emptiness of Multi-pushdown Automata Is 2ETIME-Complete , 2008, Developments in Language Theory.

[28]  Oscar H. Ibarra,et al.  Conter Machines: Decidable Properties and Applications to Verification Problems , 2000, MFCS.

[29]  Alain Finkel,et al.  Reversal-Bounded Counter Machines Revisited , 2008, MFCS.

[30]  Seymour Ginsburg,et al.  One-way stack automata , 1967, JACM.

[31]  Oscar H. Ibarra,et al.  The effect of end-markers on counter machines and commutativity , 2016, Theor. Comput. Sci..

[32]  Oscar H. Ibarra,et al.  Reversal-Bounded Multicounter Machines and Their Decision Problems , 1978, JACM.

[33]  Javier Esparza,et al.  Reachability Analysis of Pushdown Automata: Application to Model-Checking , 1997, CONCUR.

[34]  Anil Seth.  Global Reachability in Bounded Phase Multi-stack Pushdown Systems , 2010, CAV.

[35]  Tayssir Touili,et al.  On the Reachability Analysis of Acyclic Networks of Pushdown Systems , 2008, CONCUR.

[36]  Sheila A. Greibach,et al.  A note on pushdown store automata and regular systems , 1967 .

[37]  Mohamed Faouzi Atig.  From Multi to Single Stack Automata , 2010, CONCUR.

[38]  Brenda S. Baker,et al.  Reversal-Bounded Multipushdown Machines , 1974, J. Comput. Syst. Sci..

[39]  Martin Kutrib,et al.  Deterministic Stack Transducers , 2017, Int. J. Found. Comput. Sci..

[40]  Andrew Chi-Chih Yao,et al.  K + 1 heads are better than K , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[41]  Martin Kutrib,et al.  Flip-Pushdown Automata: k+1 Pushdown Reversals Are Better than k , 2003, ICALP.

[42]  Oscar H. Ibarra,et al.  Eliminating the storage tape in reachability constructions , 2003, Theor. Comput. Sci..

[43]  Oscar H. Ibarra,et al.  Characterizations of Bounded semilinear Languages by One-Way and Two-Way Deterministic Machines , 2012, Int. J. Found. Comput. Sci..

[44]  Oscar H. Ibarra,et al.  On Reachability and Safety in Infinite-State Systems , 2001, Int. J. Found. Comput. Sci..

[45]  Andrzej Blikle,et al.  Mathematical Foundations of Computer Science , 1974, Lecture Notes in Computer Science.

[46]  Martin Kutrib,et al.  Set Automata , 2016, Int. J. Found. Comput. Sci..

[47]  Oscar H. Ibarra,et al.  Binary Reachability Analysis of Discrete Pushdown Timed Automata , 2000, CAV.