5 research outputs found
Reachability in Concurrent Uninterpreted Programs
We study the safety verification (reachability problem) for concurrent programs with uninterpreted functions/relations. By extending the notion of coherence, recently identified for sequential programs, to concurrent programs, we show that reachability in coherent concurrent programs under various scheduling restrictions is decidable by a reduction to multistack pushdown automata, and establish precise complexity bounds for them. We also prove that the coherence restriction for these various scheduling restrictions is itself a decidable property
On the Separability Problem of String Constraints
We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e., I is a superset of A and disjoint from B)? The separability of string constraints is the same as the fundamental problem of interpolation for string constraints. We first show that regular separability of straight line string constraints is undecidable. Our second result is the decidability of the separability problem for straight-line string constraints by piece-wise testable languages, though the precise complexity is open. In our third result, we consider the positive fragment of piece-wise testable languages as a separator, and obtain an ExpSpace algorithm for the separability of a useful class of straight-line string constraints, and a Pspace-hardness result
Bounded Reachability Problems are Decidable in FIFO Machines
The undecidability of basic decision problems for general FIFO machines such
as reachability and unboundedness is well-known. In this paper, we provide an
underapproximation for the general model by considering only runs that are
input-bounded (i.e. the sequence of messages sent through a particular channel
belongs to a given bounded language). We prove, by reducing this model to a
counter machine with restricted zero tests, that the rational-reachability
problem (and by extension, control-state reachability, unboundedness, deadlock,
etc.) is decidable. This class of machines subsumes input-letter-bounded
machines, flat machines, linear FIFO nets, and monogeneous machines, for which
some of these problems were already shown to be decidable. These theoretical
results can form the foundations to build a tool to verify general FIFO
machines based on the analysis of input-bounded machines
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum