A Comparison of Presburger Engines for EFSM Reachability

Implicit state enumeration for extended finite state machines relies on a decision procedure for Presburger arithmetic. We compare the performance of two Presburger packages, the automata-based Shasta package and the polyhedrabased Omega package. While the raw speed of each of these two packages can be superior to the other by a factor of 50 or more, we found the asymptotic performance of Shasta to be equal or superior to that of Omega for the experiments we performed.

[1]  Günther Blaschek The Omega Library , 1994 .

[2]  Kwang-Ting Cheng,et al.  Automatic Functional Test Generation Using The Extended Finite State Machine Model , 1993, 30th ACM/IEEE Design Automation Conference.

[3]  J. R. Büchi On a Decision Method in Restricted Second Order Arithmetic , 1990 .

[4]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[5]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract) , 1995, SAS.

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

[7]  Srinivas Devadas Comparing two-level and ordered binary decision diagram representations of logic functions , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Richard Gerber,et al.  Verifying systems with integer constraints and Boolean predicates: a composite approach , 1998, ISSTA '98.

[9]  S. Sieber On a decision method in restricted second-order arithmetic , 1960 .

[10]  Tiziano Villa,et al.  VIS: A System for Verification and Synthesis , 1996, CAV.

[11]  Olivier Coudert,et al.  Verification of Synchronous Sequential Machines Based on Symbolic Execution , 1989, Automatic Verification Methods for Finite State Systems.

[12]  Gaetano Borriello,et al.  Symbolic timing verification of timing diagrams using Presburger formulas , 1997, DAC.

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

[14]  J. R. Shoenfield,et al.  Review: Herbert B. Enderton, A Mathematical Introduction to Logic , 1973 .

[15]  Richard Gerber,et al.  Symbolic Model Checking of Infinite State Systems Using Presburger Arithmetic , 1997, CAV.

[16]  Derek C. Oppen,et al.  A 2^2^2^pn Upper Bound on the Complexity of Presburger Arithmetic , 1978, J. Comput. Syst. Sci..

[17]  Kurt Keutzer,et al.  Design verification and reachability analysis using algebraic manipulation , 1991, [1991 Proceedings] IEEE International Conference on Computer Design: VLSI in Computers and Processors.

[18]  William Pugh,et al.  A practical algorithm for exact array dependence analysis , 1992, CACM.

[19]  Nils Klarlund,et al.  Mona: Decidable Arithmetic in Practice , 1996, FTRTFT.

[20]  Pierre Wolper,et al.  Symbolic Verification with Periodic Sets , 1994, CAV.