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A Note on Recursive Functions
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 1996
"... In this paper, we propose a new and elegant definition of the class of recursive functions, analogous to Kleene's definition but differing in the primitives taken, thus demonstrating the computational power of the concurrent programming language introduced in [Walters 1991, Walters 1992, Khalil and ..."
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Cited by 9 (8 self)
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In this paper, we propose a new and elegant definition of the class of recursive functions, analogous to Kleene's definition but differing in the primitives taken, thus demonstrating the computational power of the concurrent programming language introduced in [Walters 1991, Walters 1992, Khalil and Walters 1993]. The definition can be immediately rephrased for any distributive graph in a countably extensive category with products, thus allowing a wide, natural generalization of computable functions.
Locally connected recursion categories
, 2006
"... Abstract. A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of noncomplemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable ..."
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Cited by 1 (0 self)
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Abstract. A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of noncomplemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally proved. The results are generalized to nonlocally
An AutomataTheoretic Approach to Concurrency Through Distributive Categories: On Morphisms
, 1993
"... ion Definition 4.3. A mapping of automata F : X \Gamma! Y is an abstraction iff the functor F : Trans(X) \Gamma! Trans(Y) is surjective on objects and arrows. An abstraction is essentially a quotient of automata. Let us consider the following example: for any automaton X, any partition of the stat ..."
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ion Definition 4.3. A mapping of automata F : X \Gamma! Y is an abstraction iff the functor F : Trans(X) \Gamma! Trans(Y) is surjective on objects and arrows. An abstraction is essentially a quotient of automata. Let us consider the following example: for any automaton X, any partition of the states of X in two classes induces an abstraction F having as codomain the automaton 2 specified here: 0<F NaN><F NaN> // a 1<F NaN><F NaN> oo a The abstraction maps the states in each class respectively to 0 and 1. All transitions which do not change the class are mapped to the identity of 0 or 1, respectively, while a transition which changes the class is mapped to the suitable atransition of 2. As a result, each arrow of Trans(X) is mapped to an arrow of the form x a n \Gamma! y (where x; y = 0 or 1); the exponent n is equal to the number of changes of class that happened while the state transformations induced by the arrow were applied. In other words, F forgets the information ab...
Time Cutoff and the Halting Problem
, 2010
"... Abstract. This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts suppor ..."
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Abstract. This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view. In this second part, I address some of the issues raised in [Ma3] and provide their development in three contexts: a categorification of the algorithmic computations; time cutâ€“off and Anytime Algorithms; and finally, a Hopf algebra renormalization of the Halting Problem.