Efficient minimization of deterministic weak -automata

Int J Softw Tools Technol Transfer

2011

Abstract. The regular model-checking approach is a set of techniques aimed at exploring symbolically infinite state spaces. These techniques proceed by representing sets of configurations of the system under analysis by regular languages, and the transition relation between these configurations by a transformation over such languages. The set of reachable configurations can then be computed by repeatedly applying the transition relation, starting from a representation of the initial set of configurations, until a fixed point is reached.In order for this computation to terminate, it is generally needed to introduce so-called acceleration operators, the purpose of which is to explore in one computation step infinitely many paths in the transition graph of the system. A simple form of acceleration operator is one that is associated to a cycle in the transition graph, computing the set of states that can be obtained by following this cycle arbitrarily many times.The computation of acceleration operators is strongly dependent on the type of the data values that are manipulated by the system, and on the symbolic representation chosen for handling sets of such values. In this survey, we describe acceleration operators suited for the regular state-space exploration of systems relying on FIFO communication channels, as well as those based on integer and real variables.

Section: Symbolic Representation Of Data Setsmentioning

confidence: 99%

Domain-specific regular acceleration

Int J Softw Tools Technol Transfer

2011

“…Another very interesting fact is that they admit an easily computable canonical form as explained in [Löd01]. Performing those operations on general RVA is feasible, but more difficult, as discussed in [Var07] for weak deterministic Büchi automata versus general Büchi automata.…”

Section: Syntax Definition 44 a Real Vector Automaton Representing Amentioning

confidence: 99%

“…Another good property of RVA is that they can easily be minimized into a canonical form [Löd01]. By being able to minimize RVA even for intermediate results, one ensures that the number of states does not depend on history of the creation of polyhedra.…”

Section: Introductionmentioning

confidence: 99%

Implicit Real Vector Automata

Electron. Proc. Theor. Comput. Sci.

Brusten

Degbomont

2010

This thesis introduces a new data structure, the Implicit Real Vector Automaton (IRVA), suited for representing symbolically polyhedra, i.e., regions of n-dimensional space defined by finite Boolean combinations of linear inequalities. IRVA can represent exactly arbitrary convex and non-convex polyhedra, including features such as open and closed boundaries, unconnected parts, and non-manifold components. In addition, they provide efficient procedures for deciding whether a point belongs to a given polyhedron, and determining the polyhedron component (vertex, edge, facet, . . . ) that contains a point.An advantage of IRVA is that they can easily be minimized into a canonical form, which leads to a simple and efficient test for equality between represented polyhedra. Elementary IRVA representing primitive polyhedra, such as linear (in)equations and vector spaces are easily constructed and algorithms have been developed for computing Boolean combinations as well as projections of polyhedra represented by IRVA.These algorithms are illustrated by complete examples of executions as a support for the comprehension of their mechanisms.Another contribution is a first prototype implementation of an IRVA library, containing functions for building and manipulating arbitrary n-dimensional polyhedra. We reinforce the presentation of the implementation by discussing some design choices. Such choices include the use of exact arithmetic.Finally, experimental results are presented and discussed. These experiments pave the way to future adaptations and improvements.

“…However, it turns out that handling real linear arithmetic with automata does not require the full power of infinite-word automata, but can be done with a very restrictive class, namely deterministic weak automata [Sta83,MSS86,MS97]. This was shown using topological arguments in [BJW01] with two important consequences: algorithms very similar to those used for finite-word automata can be used for manipulating this class, and it admits a easily computable reduced normal form [Löd01]. Now, since it is very easy to express that a number is an integer with an automaton (its fractional part is 0), the automata-theoretic approach to handling real arithmetic can also cope with the theory in which both real and integer variables are allowed.…”

Section: Introductionmentioning

confidence: 99%

Representing Arithmetic Constraints with Finite Automata: An Overview

Wolper

2002

Logic Programming

Abstract. Linear numerical constraints and their first-order theory, whether defined over the reals or the integers, are basic tools that appear in many areas of Computer Science. This paper overviews a set of techniques based on finite automata that lead to decision procedures and other useful algorithms, as well as to a normal form, for the first-order linear theory of the integers, of the reals, and of the integers and reals combined. This approach has led to an implemented tool, which has the so far unique capability of handling the linear first-order theory of the integers and reals combined.