Mona & Fido: The Logic-Automaton Connection in Practice

We discuss in this paper how connections, discovered almost forty years ago, between logics and automata can be used in practice. For such logics expressing regular sets, we have developed tools that allow efficient symbolic reasoning not attainable by theorem proving or symbolic model checking.

[1]  Jean Vuillemin,et al.  On Circuits and Numbers , 1994, IEEE Trans. Computers.

[2]  Hubert Comon-Lundh,et al.  Diophantine Equations, Presburger Arithmetic and Finite Automata , 1996, CAAP.

[3]  Larry Joseph Stockmeyer,et al.  The complexity of decision problems in automata theory and logic , 1974 .

[4]  Nils Klarlund,et al.  Formal design constraints , 1996, OOPSLA '96.

[5]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[6]  B. L. Saec.  Saturating right congruences , 1990 .

[7]  Nils Klarlund,et al.  Mona: Monadic Second-Order Logic in Practice , 1995, TACAS.

[8]  Thomas Wilke,et al.  An Algebraic Theory for Regular Languages of Finite and Infinite Words , 1993, Int. J. Algebra Comput..

[9]  Bertrand Le Saëc.  Saturating right congruences , 1990, RAIRO Theor. Informatics Appl..

[10]  C. C. Elgot.  Decision problems of finite automata design and related arithmetics , 1961 .

[11]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[12]  Amir Pnueli,et al.  Symbolic Model Checking with Rich ssertional Languages , 1997, CAV.

[13]  John Doner,et al.  Tree Acceptors and Some of Their Applications , 1970, J. Comput. Syst. Sci..

[14]  J. Büchi.  Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[15]  Nils Klarlund.  A Homomorphism Concepts for omega-Regularity , 1994, CSL.

[16]  Chen-Shang Lin,et al.  On the OBDD-Representation of General Boolean Functions , 1992, IEEE Trans. Computers.

[17]  Aarti Gupta,et al.  Representation and symbolic manipulation of linearly inductive Boolean functions , 1993, ICCAD.

[18]  Ludwig Staiger,et al.  On Syntactic Congruences for Omega-Languages , 1997, Theor. Comput. Sci..

[19]  William I. Gasarch,et al.  Implementing WS1S via Finite Automata , 1996, Workshop on Implementing Automata.

[20]  Tiziana Margaria,et al.  MOSEL: A FLexible Toolset for Monadic Second-Order Logic , 1997, TACAS.

[21]  Nils Klarlund.  A Homomorphism Concept for omega-Regularity , 1994 .

[22]  Nils Klarlund,et al.  Algorithms for Guided Tree Automata , 1996, Workshop on Implementing Automata.

[23]  André Arnold,et al.  A Syntactic Congruence for Rational omega-Language , 1985, Theor. Comput. Sci..

[24]  Aarti Gupta,et al.  Parametric Circuit Representation Using Inductive Boolean Functions , 1993, CAV.

[25]  M. Rabin.  Decidability of second-order theories and automata on infinite trees. , 1969 .

[26]  Nils Klarlund,et al.  Automatic verification of pointer programs using monadic second-order logic , 1997, PLDI '97.

[27]  Albert R. Meyer,et al.  WEAK MONADIC SECOND ORDER THEORY OF SUCCESSOR IS NOT ELEMENTARY-RECURSIVE , 1973 .

[28]  Nils Klarlund,et al.  BDD Algortihms and Cache Misses , 1996 .

[29]  Nils Klarlund,et al.  An n log n Algorithm for Online BDD Refinement , 1995, J. Algorithms.

[30]  M. Rabin.  Decidability of second-order theories and automata on infinite trees , 1968 .

[31]  Ludwig Staiger,et al.  On Syntactic Congruences for Omega-Languages , 1993, Theor. Comput. Sci..

[32]  Nils Klarlund,et al.  Hardware Verification using Monadic Second-Order Logic , 1995, CAV.

[33]  Nils Klarlund,et al.  A Domain-Specific Language for Regular Sets of Strings and Trees , 1997, IEEE Trans. Software Eng..

[34]  Sérgio Vale Aguiar Campos,et al.  Symbolic Model Checking , 1993, CAV.