The Existence of ω\omega-Chains for Transitive Mixed Linear Relations and Its Applications

We show that it is decidable whether a transitive mixed linear relation has an $\omega$-chain. Using this result, we study a number of liveness verification problems for generalized timed automata within a unified framework. More precisely, we prove that (1) the mixed linear liveness problem for a timed automaton with dense clocks, reversal-bounded counters, and a free counter is decidable, and (2) the Presburger liveness problem for a timed automaton with discrete clocks, reversal-bounded counters, and a pushdown stack is decidable.Comment: 26 page

The Existence of omega-Chains for Transitive Mixed Linear Relations and Its Applications

We show that it is decidable whether a transitive mixed linear relation has an omega-chain. Using this result..