Abstract. We propose a remedy to that part of the state-explosion problem for timed automata which is due to interleaving of actions. We prove the following quite surprising result: the union of all zones reached by different interleavings of the same set of transitions is convex. Consequently we can improve the standard reachability computation for timed automata by merging such zones whenever they are encountered. Since passage of time distributes over union, we can continue the successor computation from the new zone and eliminate completely the explosion due to interleaving.

Abstract. In this paper we report some progress in applying timed automata technology to large-scale problems. We focus on the problem of finding maximal stabilization time for combinational circuits whose inputs change only once and hence they can be modeled using acyclic timed automata. We develop a "divideand-conquer" methodology based on decomposing the circuit into sub-circuits and using timed automata analysis tools to build conservative low-complexity approximations of the sub-circuits to be used as inputs for the rest of the system. Some preliminary results of this methodology are reported.

We present a systematic translation from timed models of genetic regulatory networks into products of timed automata to which one can apply verification tools in order learn about the possible qualitative behaviors of the network under a whole range of uncertain delay parameters. We have developed a tool chain starting from a high-level description of the network down to an exhaustive analysis of its behavior. We have demonstrated the potential applicability of this framework on several examples.

We develop and implement a methodology for automatic abstraction of systems defined as networks of timed components modeled by timed automata. The abstraction technique yields an abstract model with much less clocks and states which overapproximate the timed behavior of the concrete system. Using this technique we can analyze timed system of size beyond the capabilities of contemporary analysis tools for timed automata.

We develop a new technique for generating small-complexity abstractions of timed automata that provide an approximation of their timed input-output behavior. This abstraction is obtained by first augmenting the automaton with additional input clocks, computing the "reachable" timed automaton that corresponds to the augmented model and finally "hiding" the internal variables and clocks of the system. As a result we obtain a timed automaton that does not allow any qualitative behavior which is infeasible due to timing constraints, and which maintains a relaxed form of the timing constraints associated with the feasible behaviors. We have implemented this technique and applied it to several examples from different application domains.