BackgroundBiochemical reactions are often modelled as discrete-state continuous-time stochastic processes evolving as memoryless Markov processes. However, in some cases, biochemical systems exhibit non-Markovian dynamics. We propose here a methodology for building stochastic simulation algorithms which model more precisely non-Markovian processes in some specific situations. Our methodology is based on Constraint Programming and is implemented by using Gecode, a state-of-the-art framework for constraint solving.ResultsOur technique allows us to randomly sample waiting times from probability density functions that not necessarily are distributed according to a negative exponential function. In this context, we discuss an important case-study in which the probability density function is inferred from single-molecule experiments that describe the distribution of the time intervals between two consecutive enzymatically catalysed reactions. Noticeably, this feature allows some types of enzyme reactions to be modelled as non-Markovian processes.ConclusionsWe show that our methodology makes it possible to obtain accurate models of enzymatic reactions that, in specific cases, fit experimental data better than the corresponding Markovian models.

In this paper we present a novel condensed narrowing-like semantics that contains the minimal information which is needed to describe compositionally all possible rewritings of a term rewriting system. We provide its goal-dependent top-down definition and, more importantly, an equivalent goal-independent bottom-up fixpoint characterization.We prove soundness and completeness w.r.t. the small-step behavior of rewriting for the full class of term rewriting systems.

In this paper we propose a method to automatically infer algebraic property-oriented specifications from Term Rewriting Systems. Namely, having three semantics with suitable properties, given the source code of a TRS we infer a specification which consists of a set of most general equations relating terms that rewrite, for all possible instantiations, to the same set of constructor terms.The semantic-based inference method that we propose can cope with non-constructorbased TRSs, and considers non-ground terms. Particular emphasis is put on avoiding the generation of "redundant" equations that can be a logical consequence of other ones.

No abstract