Equational Characterization of Covariant-Contravariant Simulation and Conformance Simulation Semantics

Covariant-contravariant simulation and conformance simulation generalize plain simulation and try to capture the fact that it is not always the case that "the larger the number of behaviors, the better". We have previously studied their logical characterizations and in this paper we present the axiomatizations of the preorders defined by the new simulation relations and their induced equivalences. The interest of our results lies in the fact that the axiomatizations help us to know the new simulations better, understanding in particular the role of the contravariant characteristics and their interplay with the covariant ones; moreover, the axiomatizations provide us with a powerful tool to (algebraically) prove results of the corresponding semantics. But we also consider our results interesting from a metatheoretical point of view: the fact that the covariant-contravariant simulation equivalence is indeed ground axiomatizable when there is no action that exhibits both a covariant and a contravariant behaviour, but becomes non-axiomatizable whenever we have together actions of that kind and either covariant or contravariant actions, offers us a new subtle example of the narrow border separating axiomatizable and non-axiomatizable semantics. We expect that by studying these examples we will be able to develop a general theory separating axiomatizable and non-axiomatizable semantics.Comment: In Proceedings SOS 2010, arXiv:1008.190

A Finite Equational Base for CCS with Left Merge and Communication Merge

Using the left merge and communication merge from ACP, we present an equational base for the fragment of CCS without restriction and relabelling. Our equational base is finite if the set of actions is finite

Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy's merge is added to that language. These results raise the question of whether there is one auxiliary binary operator whose addition to CCS leads to a finite axiomatisation of bisimilarity. This study provides a negative answer to that question based on three reasonable assumptions