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Recursion schemata for NC k
"... We give a recursiontheoretic characterization of the complexity classes NC k for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (tim ..."
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Cited by 2 (1 self)
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We give a recursiontheoretic characterization of the complexity classes NC k for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time
Towards an implicit characterization of NCk
"... Abstract. We define a hierarchy of term systems T k by means of restrictions of the recursion schema. We essentially use a pointer technique together with tiering. We prove T k ⊆ NCk ⊆ T k+1, for k ≥ 2. Special attention is put on the description of T 2 and T 3 and on the proof of T 2 ⊆ NC2 ⊆ T 3. ..."
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Abstract. We define a hierarchy of term systems T k by means of restrictions of the recursion schema. We essentially use a pointer technique together with tiering. We prove T k ⊆ NCk ⊆ T k+1, for k ≥ 2. Special attention is put on the description of T 2 and T 3 and on the proof of T 2 ⊆ NC2 ⊆ T 3
Recursion Schemata For Slow Growing Depth Circuit Classes
"... . In this note we characterize iterated log depth circuit classes LD i and ND i by Cobhamlike bounded recursion schemata. We also give alternative characterizations which utilizes the safe recursion method developed by Bellantoni and Cook. 1. Introduction The search for recursion theoretic ..."
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. In this note we characterize iterated log depth circuit classes LD i and ND i by Cobhamlike bounded recursion schemata. We also give alternative characterizations which utilizes the safe recursion method developed by Bellantoni and Cook. 1. Introduction The search for recursion
RECURSION SCHEMATA FOR SLOW GROWING DEPTH CIRCUIT CLASSES
"... ABSTRACT. In this note we characterize iterated $\log $ depth circuit classes between $AC^{\mathrm{O}} $ and $AC^{1} $ by Cobhamlike bounded recursion schemata. We also give alternative characterizations which utilizes the safe recursion method developed by Bellantoni and Gook. 1. ..."
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ABSTRACT. In this note we characterize iterated $\log $ depth circuit classes between $AC^{\mathrm{O}} $ and $AC^{1} $ by Cobhamlike bounded recursion schemata. We also give alternative characterizations which utilizes the safe recursion method developed by Bellantoni and Gook. 1.
Exploiting Logic Program Schemata to Teach Recursive Programming
"... Abstract. Recursion is a complex concept that most novice logic programmers have difficulty grasping. Problems associated with recursion are avoided in imperative languages where iteration is provided as an alternative to recursion. Although difficult to learn, recursion is very easy to use once it ..."
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which are designed to incrementally improve the skills of the student. In the domain of computer programming, collaboration is an authentic activity. In this paper, we present logic program templates and schemata which add conditional recursion to logic programming languages and enable collaborative
Generalized Coiteration Schemata
, 2003
"... Coiterative functions can be explained categorically as final coalgebraic morphisms, once coinductive types are viewed as final coalgebras. However, the coiteration schema which arises in this way is too rigid to accommodate directly many interesting classes of circular specifications. In this paper ..."
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Cited by 8 (0 self)
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captures naturally a wide range of coiteration schemata, such as the duals of primitive recursion and courseofvalue iteration, and mutual coiteration. Then we show that, in the more structured categorical setting of bialgebras, T coiteration captures guarded coiterations schemata, i.e. specifications
Representing Logic Program Schemata in Prolog
 Proceedings of the Twelfth International Conference on Logic Programming
, 1995
"... Abstract. Program schemata and programming techniques provide a mechanism for representing the essential characteristics of logic programs. By abstracting out common recursive control flow patterns, program schemata capture large classes of logic programs. Programming techniques represent common pro ..."
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Cited by 14 (2 self)
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Abstract. Program schemata and programming techniques provide a mechanism for representing the essential characteristics of logic programs. By abstracting out common recursive control flow patterns, program schemata capture large classes of logic programs. Programming techniques represent common
Linear Recursion
"... s decoration does not allow for improvement as far as reductions are concerned: all functions defined by recursion are totally intuitionistic. But some functions defined on the list data type, for example "append" or "reverse", seem to be linear in their definitions and should no ..."
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natural numbers object and a linear primitive recursion schemata. Par'e and Roman in [PR89] proposed a natural numbers object in the context of symmetric monoidal closed categories, which is the usual natural numbers object definition when the cartesian product is substituted by a tensor
Representing Logic Program Schemata in lambdaProlog
"... .Program schemata and programming techniques provide a mechanism for representing the essential characteristics of logic programs. By abstracting out common recursive control flow patterns, program schemata capture large classes of logic programs. Programming techniques represent common program comp ..."
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Cited by 2 (0 self)
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.Program schemata and programming techniques provide a mechanism for representing the essential characteristics of logic programs. By abstracting out common recursive control flow patterns, program schemata capture large classes of logic programs. Programming techniques represent common program
Tailoring Recursion for Complexity
 J. SYMBOLIC LOGIC
, 1995
"... We design functional algebras that characterize various complexity classes of global functions. For this purpose, classical schemata from recursion theory are tailored for capturing complexity. In particular we present a functional analogue of firstorder logic and describe algebras of the function ..."
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Cited by 13 (1 self)
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We design functional algebras that characterize various complexity classes of global functions. For this purpose, classical schemata from recursion theory are tailored for capturing complexity. In particular we present a functional analogue of firstorder logic and describe algebras
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