Efficient Timed Reachability Analysis Using Clock Difference Diagrams

Abstract

One of the major problems in applying automatic verification tools to industrial-size systems is the excessive amount of memory required during the state-space exploration of a model. In the setting of real-time, this problem of state-explosion requires extra attention as information must be kept not only on the discrete control structure but also on the values of continuous clock variables. In this paper, we exploit Clock Difference Diagrams, CDD's, a BDD-like data-structure for representing and effectively manipulating certain nonconvex subsets of the Euclidean space, notably those encountered during verification of timed automata. A version of the real-time verification tool Uppaal using CDD's as a compact data-structure for storing explored symbolic states has been implemented. Our experimental results demonstrate significant spacesavings: for eight industrial examples, the savings are in average 42% with moderate increase in runtime. We further report on how the symbolic state-space exploration itself may be carried out using CDD's.

Improvements for the Symbolic Verification of Timed Automata

“…, (6,1) ,(7,2) , (8,3) , (9,4) , (10,5) , (6,6) , (6,0) , (8,2) ,(7,1) , (9,3) , (10,4) , (4,0) (6, 0)). After the discrete transition, only valuations of reset clocks are different from their precursors.…”

“…Besides DBMs, clock difference diagrams (CDDs) [3] and their variants [16,15] were used to combine the representation of locations and clock valuations in zones. Their common disadvantage is that the lack of a unique canonical representation may hinder the containment relation detection.…”

The Octahedron Abstract Domain

“…The first step is the definition of a relaxed version of the canonical form, which is called saturated form 4 . While the canonical form has the tightest bound in each of its inequalities, the bounds in the saturated form may be more relaxed.…”

Static Guard Analysis in Timed Automata Verification

“…using lists of zones or structures as CDDs [4], DDDs [21]), the actual computation of the closure would be at least as difficult as solving the locationreachability problem itself [1,2]. What we are looking for is an alternative abstraction obtained by a more efficient analysis of the relevance of guards.…”

“…4 Thus, to maximize abstraction in the interest of early termination, we look for a smallest solution of S A . For example, given the automaton A of Fig.…”