We introduce a notion of bisimulation for graph rewriting systems, allowing us to prove observational equivalence for dynamically evolving graphs and networks. We use the framework of synchronized graph rewriting with mobility which we describe in two different, but operationally equivalent ways: on graphs defined as syntactic judgements and by using tile logic. One of the main results of the paper says that bisimilarity for synchronized graph rewriting is a congruence whenever the rewriting rules satisfy the basic source property. Furthermore we introduce an up-to technique simplifying bisimilarity proofs and use it in an example to show the equivalence of a communication network and its specification.

. Interaction nets are graphical rewriting systems which can be used as either a high-level programming paradigm or a low-level implementation language. However, an operational semantics together with notions of strategy and normal form which are essential to reason about implementations, are not easy to formalize in this graphical framework. The purpose of this paper is to study a textual calculus for interaction nets, with a formal operational semantics, which provides a foundation for implementation. In addition, we are able to specify in this calculus various strategies, and a type system which formalizes the notion of partition used to define semi-simple nets. The resulting system can be seen as a kernel for a programming language, analogous to the -calculus. 1 Introduction Interaction nets, introduced by Lafont [12], offer a graphical paradigm of computation based on net rewriting. They have proven themselves successful for application in computer science, most notably with the ...

Many calculi, for instance the -calculus and term rewriting systems, have benefitted from extensions, especially to include data structures and operations which are more naturally defined in another language. A simple example of this is PCF where the -calculus is extended to include natural numbers and some basic functions over this type, which avoids having to use inefficient encodings of numbers. In this paper we present a generalization of interaction nets along these lines. We begin by adding a fixed set of constants and predefined functions, before presenting the main contribution of the paper which is a system of interaction nets combined with an external language where functions and richer data types can be defined. Keywords: Interaction nets, Rewriting Systems, Combinations. 1

This chapter reviews the many sources that I have relied upon in designing MIN,

The notion of contextual equivalence is fundamental in the theory of programming languages. By setting up a notion of bisimilarity, and showing that it coincides with contextual equivalence, one obtains a simple coinductive proof technique for showing that two programs are equivalent in all contexts. In this paper we apply these (now standard) techniques to interactions nets, a graphical programming language characterized by local reduction. This work generalizes previous studies of operational equivalence in interaction nets since it can be applied to untyped systems, thus all systems of interaction nets are captured.