Primitive Recursive Selection Functions over Abstract Algebras

2006 ◽  
pp. 595-606
Author(s):  
J. I. Zucker
Keyword(s):  
Primitive Recursive

scholarly journals Towards efficient verification of population protocols

2021 ◽  
Author(s):  
Michael Blondin ◽  
Javier Esparza ◽  
Stefan Jaax ◽  
Philipp J. Meyer
Keyword(s):  
Linear Constraints ◽  
Computational Power ◽  
High Complexity ◽  
Reachability Problem ◽  
Population Protocols ◽  
Finite State ◽  
State Agents ◽  
Efficient Verification ◽  
Primitive Recursive ◽  
Very High

AbstractPopulation protocols are a well established model of computation by anonymous, identical finite-state agents. A protocol is well-specified if from every initial configuration, all fair executions of the protocol reach a common consensus. The central verification question for population protocols is the well-specification problem: deciding if a given protocol is well-specified. Esparza et al. have recently shown that this problem is decidable, but with very high complexity: it is at least as hard as the Petri net reachability problem, which is -hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class $${ WS}^3$$ WS 3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that $${ WS}^3$$ WS 3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership and correctness problems for $${ WS}^3$$ WS 3 reduce to solving boolean combinations of linear constraints over $${\mathbb {N}}$$ N . This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.

Simplifications of the recursion scheme

1971 ◽  
Vol 36 (4) ◽  
pp. 653-665 ◽  
Author(s):  
M. D. Gladstone
Keyword(s):  
Recursion Scheme ◽  
Projection Functions ◽  
Primitive Recursive

This paper resolves 3 problems left open by R. M. Robinson in [3].We recall that the set of primitive recursive functions is the closure under (i) substitution (or “composition”), and (ii) recursion, of the set P consisting of the zero, successor and projection functions (see any textbook, for instance p. 120 of [2]).

scholarly journals Primitive recursive computations.

1967 ◽  
Vol 8 (4) ◽  
pp. 311-317 ◽  
Author(s):  
Stephen H. McCleary
Keyword(s):  
Primitive Recursive

Chess Is Primitive Recursive

2021 ◽  
pp. 421-434
Author(s):  
Vladimir A. Kulyukin
Keyword(s):  
Primitive Recursive

A Hierarchy on the Class of Primitive Recursive Ordinal Functions

1976 ◽  
Vol 28 (6) ◽  
pp. 1205-1209
Author(s):  
Stanley H. Stahl
Keyword(s):  
Natural Numbers ◽  
Recursive Functions ◽  
Set Functions ◽  
Primitive Recursive ◽  
Class Of Functions ◽  
Recursive Set

The class of primitive recursive ordinal functions (PR) has been studied recently by numerous recursion theorists and set theorists (see, for example, Platek [3] and Jensen-Karp [2]). These investigations have been part of an inquiry concerning a larger class of functions; in Platek's case, the class of ordinal recursive functions and in the case of Jensen and Karp, the class of primitive recursive set functions. In [4] I began to study PR in depth and this paper is a report on an attractive analogy between PR and its progenitor, the class of primitive recursive functions on the natural numbers (Prim. Rec).

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