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Rewriting On Cyclic Structures: Equivalence Between The Operational And The Categorical Description
, 1999
"... . We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, fo ..."
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Cited by 13 (6 self)
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. We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut 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 2theorie 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...
Traced Premonoidal Categories
, 1999
"... Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a wellknown theorem relating trace ..."
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Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a wellknown theorem relating traces and Conway operators in cartesian categories.
Čirovič, On some equivalence notions of synchronous systems
 Proceedings, 11th International Conference on Automata and Formal Languages, Dogogókő, Hungary
, 2005
"... An important optimization tool in the design of synchronous systems is retiming, which in many cases allows a significant reduction in the length of the systems ’ clock period. Even though the internal structure of systems changes upon retiming, their inputoutput behavior remains essentially the sa ..."
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An important optimization tool in the design of synchronous systems is retiming, which in many cases allows a significant reduction in the length of the systems ’ clock period. Even though the internal structure of systems changes upon retiming, their inputoutput behavior remains essentially the same. The original system and the one after the retiming can simulate each other in a suitable way. The equivalence notion arising from this kind of mutual simulation is called simulation equivalence, and the aim of this paper is to characterize simulation equivalence in an algebraic setting. It is shown that simulation equivalence is a congruence relation of the algebra of synchronous schemes, and that this congruence is the smallest one containing retiming equivalence and finitary strong equivalence. An axiomatization of these equivalences is presented in the general framework of strictly monoidal categories with feedback. 1
Simulation equivalence of automata and circuits
"... Automata over a symmetric monoidal category M are introduced, and a multistep simulation is defined among such automata. The collection of Mautomata is given the structure of a 2category on the same objects as M, in which the vertical structure is determined by groups of indistinguishable simula ..."
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Automata over a symmetric monoidal category M are introduced, and a multistep simulation is defined among such automata. The collection of Mautomata is given the structure of a 2category on the same objects as M, in which the vertical structure is determined by groups of indistinguishable simulations. TwoMautomata are called simulation equivalent if they are connected by an isomorphism of 2cells in this 2category. It is shown that the category of simulation equivalent Mautomata is monoidal, and it satisfies all the axioms of traced monoidal categories, except the one that explicitly kills the delay. 1