Global Reachability in Bounded Phase Multi-stack Pushdown Systems

Abstract

Bounded phase multi-stack pushdown systems (mpds) have been studied recently. Given a set C of configurations of a mpds M, let pre * M (C, k) be the set of configurations of M from which M can reach an element of C in at most k phases. In this paper, we show that for any mpds M, any regular set C of configurations of M and any number k, the set pre * M (C, k), is regular. We use saturation like method to construct a non-deterministic finite multi-automaton recognizing pre * M (C, k). Size of the automaton constructed is double exponential in k which is optimal as the worst case complexity measure.

MSO Decidability of Multi-Pushdown Systems via Split-Width

“…In all these cases, the control state reachability problem is known to be decidable. Further, a stronger version known as the global reachability problem is also decidable -given a regular set of configurations compute the pre * of this set [2,3,16,24].…”

Model-Checking of Ordered Multi-Pushdown Automata

“…Next, we state our main theorem which is a generalization of the result obtained in for bounded-phase visibly multi-stack pushdown automata [Set10].…”

“…Symbolic representation of MPA configurations. We show in this section how we can symbolically represent infinite sets of multi-pushdown automaton configurations using special kind of finite automata which were introduced in [Set10]. Let M = (n, Q, Σ, Γ, ∆, q 0 , γ 0 , F ) be a multi-pushdown automaton.…”

“…Therefore, our first task is to find a finite symbolic representation of the possibly infinite state-space of an ordered multi-pushdown automaton. For that, we consider the class of recognizable sets of configurations defined using finite state automata [QR05,ABT08,Set10].…”

Ordered Pure Multi-Pushdown Automata

“…In [5], pure multi-pushdown automata that perform complete pushdown pops are introduced and studied. Papers [14,15,16,17] from the area of formal verification study multi-pushdown automata with ordered pushdowns, where the pop operation can be performed only on the first nonempty pushdown.…”