Timed pushdown automata and branching vector addition systems

Binary Reachability of Timed-register Pushdown Automata and Branching Vector Addition Systems

“…The following is our first major result. Since the reachability relation is characterised in a decidable logic, the non-emptiness problem reduces to satisfiability and we obtain the following corollary, which is one of the main results of the original communication [15]. Proof.…”

“…Notwithstanding the increased expressive power gained by removing the orbit-finite restriction ( †), decidability is preserved. We have shown in our previous communication that non-emptiness of trPDA is in 2-ExpTime and ExpTime-hard [15,Theorem 1], under the somewhat technical assumption that the stack alphabet be orbit finite, i.e., there must exists a bound K ∈ N on the span of stack symbols Γ ′ = Γ × (Z k ) span≤K × Q l . (The orbit-finite restriction on the input alphabet is inessential for non-emptiness, since the input is existentially quantified and thanks to elimination of quantifiers of Theorem 3.1.)…”

“…Step 4: Simplify ψ 2 . Cases 1 and 2 are unchanged, and thus ψ 1 is the same as from (15) and ψ 2 from (16). For ψ 3 , ψ 4 we perform the following modifications.…”

“…Full version. This article is a new and full version of the preliminary conference paper [15], embodying a complete revision and a major extension. The main novelties in comparison with the former work are: (1) We show an effective logical characterisation of the binary reachability relations of trPDA, instead of merely deciding non-emptiness.…”

Timed Systems through the Lens of Logic

“…Several variants and extensions of this basic model have been considered over the years, for instance using event-clocks [8] or diagonal constraints, or even by allowing (non-) deterministic updates of clocks. Subsequently, there has been a growing body of work [2,1,5,6,14,15,16,17,25] towards adding auxiliary data structures like stacks [27,4,3] or queues [3] to such timed automata. In all these, the techniques used to solve the emptiness problem were specific and tailor-made to the choice of the data structure, kind of constraints and updates that are allowed.…”