Abstract not found

. We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2-theories. We show that this presentation is equivalent to the well-accepted operational definition proposed by Barendregt et alii---but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms. R'esum'e. Nous pr'esentons une formulation cat'egorique de la r'e'ecriture des graphes cycliques des termes, bas'ee sur une variante de 2-theorie alg'ebrique. Nous prouvons que cette pr'esentation est 'equivalente `a la d'efinition op'erationnelle propos'ee par Barendregt et d'autres auteurs, mais pas dons le cas des radicaux circulaires, pour lesquels nous proposons (et justifions formellem...

Abstract. Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a ‘universal ’ LMP as the spectrum of a commutative C ∗-algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the universal LMP as the set of homomorphims from an ordered commutative monoid of labelled trees into the multiplicative with respect to probabilistic bisimilarity. We also consider LMPs with entry points and exit points in the setting of iteration theories. We define an iteration theory of LMPs by specifying its categorical dual: a certain category of C ∗-algebras. We find that the basic operations for composing LMPs have simple definitions in the dual category. 1

Abstract not found