A comparison of Presburger engines for EFSM reachability

Abstract

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.

MONA Implementation Secrets

“…euclid.mona -an encoding in Presburger arithmetic of six steps of reachability on a machine that implements Euclid's GCD algorithm [45]. Provided by Tom Shiple.…”

“…In an independent comparison [45] it was noted that Mona was consistently twice as fast as a specially designed automaton package based on a BDD package considered efficient. In [33], the comparison to a traditional BDD package yielded a factor 5 speedup.…”

“…Happily, many interesting projects fit into this niche, including hardware verification [4,1], pointer analysis [23,17], controller synthesis [44,22], natural languages [39], parsing tools [14], software design descriptions [29], Presburger arithmetic [45], and verification of concurrent systems [32,31,24,42,46].…”

“…The Shasta tool from 1998 is based upon the same ideas as Mona. It is used as an engine for Presburger Arithmetic [45].…”

Global vs. local model checking: a comparison of verification techniques for infinite state systems

“…The translation of arithmetics to finite automata goes back to Büchi [10] (see also [2,4,35]). A comparison of Presburger decision procedures for reachability analysis can be found in [30].…”