Computer Science Logic 

Abstract: The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behavior has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.

Abstract: We consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-teachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n(|δ(A)| + |W max |)), where n is the number of clocks, |δ(A)| is the size of the clock constraints and |W max | is the size of the largest weight. We show that this algorithm can be improved, if we restrict to weighted timed automata with a single clock. In case we consider a single starting state for the optimal-reachability problem, our approach yields an algorithm that takes exponential time only in the length of clock constraints.

Abstract: In a data word or a data tree each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been considered in the realm of semistructured data, timed automata and extended temporal logics. This paper survey several know results on automata and logics manipulating data words and data trees, the focus being on their relative expressive power and decidability.

Abstract: Kleene algebras with tests provide a rigorous framework for equational specification and verification They have been used successfully in basic safety analysis, source-to-source program transformation, and concurrency control We prove the completeness of the equational theory of Kleene algebra with tests and *-continuous Kleene algebra with tests over language-theoretic and relational models We also show decidability Cohen''s reduction of Kleene algebra with hypotheses of the form $r=0$ to Kleene algebra without hypotheses is simplified and extended to handle Kleene algebras with tests