Polymorphic Systems with Arrays, 2-Counter Machines and Multiset Rewriting

Abstract

Polymorphic systems with arrays (PSAs) is a general class of nondeterministic reactive systems. A PSA is polymorphic in the sense that it depends on a signature, which consists of a number of type variables, and a number of symbols whose types can be built from the type variables. Some of the state variables of a PSA can be arrays, which are functions from one type to another. We present several new decidability and undecidability results for parameterised control-state reachability problems on subclasses of PSAs.

Nets with Tokens Which Carry Data

“…Thus, question (1) posed above is answered positively. The decidability of coverability for data nets subsumes the results in [6,10,14,11,12,13,15,16,17] that coverability is decidable for the respective classes of infinite-state systems mentioned above, and in most cases the proof in this paper is more succinct.…”

“…That leaves open whether we have non-elementarity for 1, 1-safe unordered Petri data nets. That class suffices for expressing polymorphic systems with one array of type X, = → Y, = without whole-array operations [16,17].…”

“…By translating Petri data nets and unordered Petri data nets to subclasses of systems in [11,12,13,16,17], the two hardness results yield the same lower bounds for corresponding decision problems for such subclasses. In particular, we obtain non-elementariness of verifying monadic multiset rewriting specifications with only equality constraints [11] and of verifying polymorphic systems with two arrays of types X, = → Y, = and X, = → {1, .…”

“…A variety of other examples of systems expressible using data nets can be found in [10,14,11,12,13,15,16], including a real-timed mutual exclusion protocol, a distributed authentication protocol, a communication protocol over unreliable channels, and a leader election algorithm.…”

On the Decidability of the Safety Problem for Access Control Policies

“…This observation allowed us to use techniques developed for data-independent systems with arrays [10,14] and apply them to access control matrices. There are other results about array systems that we believe can be leveraged to analyse access control policies, in particular results about arrays with reset [16,11].…”