Complexity of Primitive Recursion

1999 ◽  
pp. 273-300 ◽  
Author(s):  
W. G. Handley ◽  
S. S. Wainer
Keyword(s):  
Primitive Recursion

Iteration of relative primitive recursion

1966 ◽  
Vol 167 (1) ◽  
pp. 53-55 ◽  
Author(s):  
Paul Axt
Keyword(s):  
Primitive Recursion

On list primitive recursion and the complexity of computinginf

1992 ◽  
Vol 32 (1) ◽  
pp. 5-9 ◽  
Author(s):  
Loïc Colson
Keyword(s):  
Primitive Recursion

The realm of primitive recursion

1988 ◽  
Vol 27 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Harold Simmons
Keyword(s):  
Primitive Recursion

scholarly journals Primitive recursive algebraic theories and program schemes

1977 ◽  
Vol 17 (2) ◽  
pp. 207-233 ◽  
Author(s):  
W. Kühnel ◽  
J. Meseguer ◽  
M. Pfender ◽  
I. Sols
Keyword(s):  
Programming Language ◽  
Generation Process ◽  
Recursive Functions ◽  
Algebraic Theories ◽  
Primitive Recursion ◽  
Recursive Theory ◽  
Carry Over ◽  
Primitive Recursive

We introduce primitive recursion as a generation process for arrows of algebraic theories in the sense of Lawvere and carry over important results on algebraic theories and functorial semantics to the enriched setting of “primitive recursive algebra”: existence of free primitive recursive theories and of theories presented by operations and equations on primitive recursive functions; existence of free models presented by generators and equations. Finally semantical correctness of translations is reduced to correctness for the basic operations. There is a connection to the theory of program schemes: program schemes involving primitive recursion correspond to arrows of a primitive recursive theory freely generated over a graph of basic operations. This theory T can be viewed as a programming language with “arithmetics” given by the basic operations and with DO-loops. A machine loaded with a compiler for T can be interpreted as a T-model in Lawvere's sense, preserving primitive recursion.

scholarly journals Strictly orthogonal left linear rewrite systems and primitive recursion

2001 ◽  
Vol 108 (1-3) ◽  
pp. 79-101 ◽  
Author(s):  
E.A. Cichon ◽  
E. Tahhan-Bittar
Keyword(s):  
Rewrite Systems ◽  
Primitive Recursion

scholarly journals Primitive recursion for higher-order abstract syntax

2001 ◽  
Vol 266 (1-2) ◽  
pp. 1-57 ◽  
Author(s):  
Carsten Schürmann ◽  
Joëlle Despeyroux ◽  
Frank Pfenning
Keyword(s):  
Higher Order ◽  
Abstract Syntax ◽  
Primitive Recursion

Boolean Role Inclusions in DL-Lite With and Without Time

2020 ◽  
Author(s):  
Roman Kontchakov ◽  
Vladislav Ryzhikov ◽  
Frank Wolter ◽  
Michael Zakharyaschev
Keyword(s):  
Description Logic ◽  
Expressive Power ◽  
Necessary Condition ◽  
Data Complexity ◽  
Temporal Dimension ◽  
Complexity Level ◽  
Primitive Recursion ◽  
Lower Complexity ◽  
Computational Properties

Traditionally, description logic has focused on representing and reasoning about classes rather than relations (roles), which has been justified by the deterioration of the computational properties if expressive role inclusions are added. The situation is even worse in the temporalised setting, where monodicity is viewed as an almost necessary condition for decidability. We take a fresh look at the description logic DL-Lite with expressive role inclusions, both with and without a temporal dimension. While we confirm that full Boolean expressive power on roles leads to FO^2-like behaviour in the atemporal case and undecidability in the temporal case, we show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to much lower complexity in the atemporal case and to decidability (and ExpSpace-completeness) in the temporal case, even if one admits full Booleans on concepts. The latter result is one of very few instances breaking the monodicity barrier in temporal FO. This is also reflected on the data complexity level, where we obtain new rewritability results into FO with relational primitive recursion and FO with unary divisibility predicates.

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