Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Implementation relations for testing through asynchronous channels

This paper concerns testing from an input output transition system (IOTS) model of a system under test that interacts with its environment through asynchronous first in first out (FIFO) channels. It explores methods for analysing an IOTS without modelling the channels. If IOTS M produces sequence $\sigma$ then, since communications are asynchronous, output can be delayed and so a different sequence might be observed. Thus M defines a language Tr(M) of sequences that can be observed when interacting with M through FIFO channels. We define implementation relations and equivalences in terms of Tr(M): an implementation relation says how IOTS N must relate to IOTS M in order for N to be a correct implementation of M. It is important to use an appropriate implementation relation since otherwise the verdict from a test run might be incorrect and because it influences test generation. It is undecidable whether IOTS N conforms to IOTS M and so also whether there is a test case that can distinguish between two IOTSs. We also investigate the situation in which we have a finite automaton P and either wish to know whether $Tr(M) \cap L(P)$ is empty or whether Tr(M) \cap \tr(P) is empty and prove that these are undecidable. In addition, we give conditions under which conformance and intersection are decidable.This work was partially supported by EPSRC grant EP/G04354X/1:The Birth, Life and Death of Semantic Mutants

On the Control of Asynchronous Automata

The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem,where both the plant and the controllers are modeled as asynchronous automataand the controllers have causal memoryis a challenging open problem.There exist three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when the dependency graph of actions is series-parallel, when the processes are connectedly communicating and when the dependency graph of processes is a tree. We design a class of plants, called decomposable games, with a decidable controller synthesis problem.This provides a unified proof of the three existing decidability results as well as new examples of decidable plants

Languages of Dot-depth One over Infinite Words

Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order, successor, minimum, and maximum predicates. Knast (1983) has shown that it is decidable whether a language has dot-depth one. We extend Knast's result to infinite words. In particular, we describe the class of languages definable in alternation-free first-order logic over infinite words, and we give an effective characterization of this fragment. This characterization has two components. The first component is identical to Knast's algebraic property for finite words and the second component is a topological property, namely being a Boolean combination of Cantor sets. As an intermediate step we consider finite and infinite words simultaneously. We then obtain the results for infinite words as well as for finite words as special cases. In particular, we give a new proof of Knast's Theorem on languages of dot-depth one over finite words.Comment: Presented at LICS 201