Verification of Timed Automata via Satisfiability Checking

Abstract

In this paper we show how to translate bounded-length verification problems for timed automata into formulae in difference logic, a propositional logic enriched with timing constraints. We describe the principles of a satisfiability checker specialized for this logic that we have implemented and report some preliminary experimental results.

Fast and Flexible Difference Constraint Propagation for DPLL(T)

“…Difference constraints can express naturally a variety of timing-related problems including schedulability, circuit timing analysis, and bounded model checking of timed automata [16,3]. In addition, difference constraints can be used as an abstraction for general linear constraints and many problems involving general linear constraints are dominated by difference constraints.…”

A Boolean Approach to Unbounded, Fully Symbolic Model Checking of Timed Automata

“…Containment of one set of states, 4> n ew, in another, (fr o id, is checked by deciding the validity of the SL formula <j> = (f) new ==> (/) O M (or equivalently, the satisfiability of -i0). There are several procedures that can decide separation formulas (e.g., [17,4,15]). …”

“…Many fully symbolic, but bounded model checking methods based on SAT have been developed recently (e.g., [5,15]). These algorithms cannot be directly extended to perform unbounded model checking.…”

Specification and Model Checking of Temporal Properties in Time Petri Nets and Timed Automata

“…Therefore, existing verification techniques frequently apply symbolic representations of state spaces using either operations on Difference Bound Matrices [34], variations of Boolean Decision Diagrams [11,84,84], or SAT-related algorithms. The latter can exploit either a sequence of translations starting from timed automata and TCTL, going via (quantified) separation logic to quantified propositional logic and further to propositional logic [10,57,73] or a direct translation from timed automata and TCTL to propositional logic [63,86,92]. Finite state spaces, preserving properties to be checked, are usually built using detailed region approach or (possibly minimal) abstract models based on state classes or regions.…”