On the decidability and complexity of the structural congruence for beta-binders

AbstractBeta-binders is a recent process calculus developed for modelling and simulating biological systems. As usual for process calculi, the semantic definition heavily relies on a structural congruence. The treatment of the structural congruence is essential for implementation. We present a subset of the calculus for which the structural congruence is decidable and a subset for which it is also efficiently solvable. The obtained results are a first step towards implementations

Algorithms for Extended Alpha-Equivalence and Complexity

Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-binding “let ” may make alpha-equivalence as hard as finding graph-isomorphisms, and that the replication operator in the pi-calculus may lead to an EXPSPACE-hard alpha-equivalence problem

On the Decidability and Complexity of the Structural Congruence for Beta-binders

Beta-binders is a recent process algebra developed for modeling and simulating biological systems. As usual for process calculi, the semantic definition heavily relies on a structural congruence. The treatment of the structural congruence is essential for implementation. The proof of the decidability of this congruence, reported in this paper, is a first step towards implementations. Published in TCS 404(1-2):156-169, c2008 Elsevier, available at http://dx.doi.org/10.1016/j.tcs.2008.04.00