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Extending the Loop Language with HigherOrder Procedural Variables
 Special issue of ACM TOCL on Implicit Computational Complexity
, 2010
"... We extend Meyer and Ritchie’s Loop language with higherorder procedures and procedural variables and we show that the resulting programming language (called Loop ω) is a natural imperative counterpart of Gödel System T. The argument is twofold: 1. we define a translation of the Loop ω language int ..."
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We extend Meyer and Ritchie’s Loop language with higherorder procedures and procedural variables and we show that the resulting programming language (called Loop ω) is a natural imperative counterpart of Gödel System T. The argument is twofold: 1. we define a translation of the Loop ω language into System T and we prove that this translation actually provides a lockstep simulation, 2. using a converse translation, we show that Loop ω is expressive enough to encode any term of System T. Moreover, we define the “iteration rank ” of a Loop ω program, which corresponds to the classical notion of “recursion rank ” in System T, and we show that both translations preserve ranks. Two applications of these results in the area of implicit complexity are described. 1
Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A COMPLETE CHARACTERIZATION OF PRIMITIVE RECURSIVE INTENSIONAL BEHAVIOURS
"... Abstract. We give a complete characterization of the class of functions that are the intensional behaviours of Primitive Recursive algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unari ..."
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Abstract. We give a complete characterization of the class of functions that are the intensional behaviours of Primitive Recursive algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers. AMS Subject Classification. — Give AMS classification codes —. 1.
Classes of Algorithms: Formalization and Comparison
, 2012
"... We discuss two questions about algorithmic completeness (in the operational sense). First, how to get a mathematical characterization of the classes of algorithms associated to the diverse computation models? Second, how to define a robust and satisfactory notion of primitive recursive algorithm? We ..."
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We discuss two questions about algorithmic completeness (in the operational sense). First, how to get a mathematical characterization of the classes of algorithms associated to the diverse computation models? Second, how to define a robust and satisfactory notion of primitive recursive algorithm? We propose solutions based on Gurevich’s Abstract State Machines. Contents 1