FAST Extended Release

Abstract

Fast is a tool designed for the analysis of counter systems, i.e. automata extended with unbounded integer variables. Despite the reachability set is not recursive in general, Fast implements several innovative techniques such as acceleration and circuit selection to solve this problem in practice. In its latest version, the tool is built upon an open architecture: the Presburger library is manipulated through a clear and convenient interface, thus any Presburger arithmetics package can be plugged to the tool. We provide four implementations of the interface using Lash, Mona, Omega and a new shared automata package with computation cache. Finally new features are available, like different acceleration algorithms.

Fast Acceleration of Ultimately Periodic Relations

“…Moreover, we need to ensure that all guards up to (and including) the (k − 1)-th step are satisfied, i.e. φ h (A h ⊗ ℓ ⊗ x h ), for all 0 ≤ ℓ < k. For the rest of the section we fix A and b, as in (4). The encoding of a consistent affine transformation T is defined as…”

“…The experimental comparison with the FAST tool [4] for difference bounds relations shows that large relations (> 50 variables), causing FAST to run out of memory, can now be handled by our implementation in less than 8 seconds, on average. We currently do not have a full implementation of the finite monoid affine transformation class, which is needed in order to compare our method with tools like FAST [4], LASH [14], or TReX [2], for this class of relations.…”

“…If R is ultimately periodic, such values are guaranteed to exist. The dove-tailing enumeration on lines 1 and 2 is guaranteed to yield the smallest value c for which the sequence is shown to be periodic 4 . Second, the algorithm attempts to compute the first rate of the sequence (line 6), by comparing the matrices σ(R b ), σ(R c+b ) and σ(R 2c+b ).…”

Model-checking CTL* over flat Presburger counter systems

“…Important cases of such transition systems with computable reachability have been established in (Ibarra, 1978;Fribourg et al, 1997;Comon et al, 1998;Finkel et al, 2000;Finkel et al, 2002). The method of acceleration for computing reachability sets has been developed in (Boigelot, 1998;Leroux, 2003) and is implemented in the verification tool FAST (Leroux, 2003;Bardin et al, 2004;Bardin et al, 2006b); see also the verification tools LASH (Boigelot, 1998) and TReX (Annichini et al, 2001).…”

Convex Hull of Arithmetic Automata

“…Intuitively, the automaton minimization algorithm performs like a simplification procedure for FO (R, Z, +, ≤). In particular arithmetic automata are adapted to the symbolic model checking approach computing inductively reachability sets of systems manipulating counters [BLP06] and/or clocks [BH06]. In practice algorithms for effectively computing an arithmetic automaton encoding the solutions of formulas in FO (R, Z, +, ≤) have been recently successfully implemented in tools Lash and Lira [BDEK07].…”