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Algorithms With Polynomial Interpretation Termination Proof
 Journal of Functional Programming
, 1999
"... We study the effect of polynomial interpretation termination proofs of deterministic (resp. nondeterministic) algorithms defined by confluent (resp. nonconfluent) rewrite systems over data structures which include strings, lists and trees, and we classify them according to the interpretations of t ..."
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Cited by 14 (3 self)
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We study the effect of polynomial interpretation termination proofs of deterministic (resp. nondeterministic) algorithms defined by confluent (resp. nonconfluent) rewrite systems over data structures which include strings, lists and trees, and we classify them according to the interpretations of the constructors. This leads to the definition of six classes which turn out to be exactly the deterministic (resp. nondeterministic) polytime, linear exponentialtime and doubly linear exponential time computable functions when the class is based on conuent (resp. nonconfluent) rewrite systems. We also obtain a characterisation of the linear space computable functions. Finally, we demonstrate that functions with exponential interpretation termination proofs are superelementary.
Programmability of Chemical Reaction Networks
"... Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard c ..."
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Cited by 9 (2 self)
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Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and
SGDLScheme: a high level algorithmic language for projective solid modeling programming
, 2000
"... The SGDL/Scheme language, which is an absolutely pure functional language for volume programming, is a geometric extension of Scheme. It achieves a natural integration of the notions of volume and programming in a powerful algorithmic system. This capability of phrasing volume expressions by way of ..."
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Cited by 2 (0 self)
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The SGDL/Scheme language, which is an absolutely pure functional language for volume programming, is a geometric extension of Scheme. It achieves a natural integration of the notions of volume and programming in a powerful algorithmic system. This capability of phrasing volume expressions by way of arithmetic expressions is the foundation of this new solid modeling system. 1 Introduction Traditionally, geometric modeling systems base their algorithmic strategies upon Euclidean geometry, and topology or set theory, ([2]). On the other hand, when they are languageoriented they obey to a 3D object description scheme using euclidean surfaces as primitives and grammatical production rules as structural relationships descriptors,([1], [7],[8]). The basic principles used by SGDL, ([9],[10]),clearly break with those of conventional systems. The primitive recursive functions,([6], [3], [11]), denoted by PRF in the following, form the basis of the functiontheoretic models and they make the li...
An Hierarchy of Terminating Algorithms With Semantic Interpretation Termination Proofs
, 1998
"... We study deterministic (nondeterministic) algorithms define by mean of confluent (resp. nonconuent) rewrite system admitting polynomial interpretation termination proofs. Data structures of the algorithms include strings, lists and trees. We classify them according to the interpretations of constr ..."
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Cited by 1 (1 self)
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We study deterministic (nondeterministic) algorithms define by mean of confluent (resp. nonconuent) rewrite system admitting polynomial interpretation termination proofs. Data structures of the algorithms include strings, lists and trees. We classify them according to the interpretations of constructors This leads to the definition of six classes, which turn out to be exactly the deterministic (nondeterministic) polytime, linear exponentialtime and doubly linear exponential time computable functions when the class is based on confluent (resp. nonconfluent) systems. Next, we demonstrate that functions with exponential interpretation termination proofs are superelementary.
D.2.8 [Software Engineering]: Metrics—complexity measures,
"... f(0, y) = g(y) f(x + 1, y) = h(x, y, f(j1(x), y),..., f(jk(x), y) where g, h, j1,..., jk are primitive recursive and ji(x) ≤ x for i ∈ {1,..., k} , are themselves primitive recursive. A similar remark holds for recursion with parameter substituhal00642731, ..."
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f(0, y) = g(y) f(x + 1, y) = h(x, y, f(j1(x), y),..., f(jk(x), y) where g, h, j1,..., jk are primitive recursive and ji(x) ≤ x for i ∈ {1,..., k} , are themselves primitive recursive. A similar remark holds for recursion with parameter substituhal00642731,
unknown title
"... SGDLScheme: a high level algorithmic language for projective solid modeling programming ..."
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SGDLScheme: a high level algorithmic language for projective solid modeling programming
1 Contents
"... 1. Il quadro storico 7 2. Una prima classificazione 9 3. Il presente volume 10 ..."
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1. Il quadro storico 7 2. Una prima classificazione 9 3. Il presente volume 10
Scaled regression: a framework for functional program termination
"... The template of primitiverecursion (PR) is powerful enough to program all functions of interest, but very few natural algorithms. Indeed, PR is justified by induction on a single argument, whereas most algorithms are seen to terminate by induction on measures which are rarely as trivial as the size ..."
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The template of primitiverecursion (PR) is powerful enough to program all functions of interest, but very few natural algorithms. Indeed, PR is justified by induction on a single argument, whereas most algorithms are seen to terminate by induction on measures which are rarely as trivial as the size of one particular input value. We explore here a framework for crafting terminating functional programs, that extends primitiverecursion while preserving its methodological benefits. In particular, we allow inductive measures, dubbed scales, that may involve several arguments, and may be different for each function. In addition, to permit such measures to refer to previously defined functions, we associate with each function an index, which carries a rough bound on the function’s sizechanging behavior. As a functional program is incrementally developed, scales are used to guarantee termination (given previous indices), and new indices are computed from previous ones, for future use.
Dispense per il corso di Dicembre 2001—Luglio 2003
"... 2. Una prima classificazione 9 3. Il presente volume 10 ..."