Representing Arithmetic Constraints with Finite Automata: An Overview
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
SAS '95 Proceedings of the Second International Symposium on Static Analysis
A Comparison of Presburger Engines for EFSM Reachability
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Counting the solutions of Presburger equations without enumerating them
Theoretical Computer Science - Implementation and application automata
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A BDD-Like implementation of an automata package
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
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This work studies automata-based symbolic data structures for representing infinite sets. Such structures are used in particular by verification tools in order to represent the sets of configurations handled during symbolic exploration of infinite state spaces. Our goal is to develop an efficient projection operator for these representations. There are several needs for such an operator during state-space exploration; we focus here on projecting the set of reachable configurations obtained at the end of exploration. An interesting application is the state-space visualization problem, which consists in providing the user with a graphical picture of a relevant fragment of the reachable state space. For theoretical reasons, the projection of automata-represented sets is inherently costly. The contribution of this paper is to introduce an improved automata-based data structure that makes it possible to reduce in several cases the effective cost of projection. The idea is twofold. First, our structure allows to apply projection to only a part of an automaton, in cases where a full computation is not necessary. Second, the structure is able to store the results of past projection operations, and to reuse them in order to speed up subsequent computations. We show how our structure can be applied to the state-space visualization problem, and discuss some experimental results.