## INTENSIONAL PROPERTIES OF POLYGRAPHS

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Citations: | 5 - 0 self |

### BibTeX

@MISC{Bonfante_intensionalproperties,

author = {Guillaume Bonfante and Yves Guiraud},

title = {INTENSIONAL PROPERTIES OF POLYGRAPHS},

year = {}

}

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### Abstract

Abstract – We present Albert Burroni’s polygraphs as a computational model, showing how these objects can be seen as functional programs. First, we prove that the model is Turing complete. Then, we use a notion of termination proof introduced by the second author to characterize polygraphs that compute in polynomial time and, going further, polynomial time functions. 1

### Citations

525 |
Theory of Self-Reproducing Automata
- Neumann
- 1966
(Show Context)
Citation Context ...mputational model. Roughly speaking, computations are done by a net of cells which individually behave according to some local transition rules: this model is close to von Neumann’s cellular automata =-=[10]-=- and Lafont’s interaction nets [7]. While von Neumann’s automata are essentially synchronous, interaction nets and polygraphs are asynchronous. The difference between the last two models is that polyg... |

113 |
On proving term rewriting systems are noetherian
- Lankford
- 1979
(Show Context)
Citation Context ...ysis tools using algebraic constructions. Here we use polynomial interpretations, but the ones we consider are somewhat different and finer than the ones traditionally used for term rewriting systems =-=[9]-=-. Let us recall that, in the term rewriting framework, polynomial interpretations gave rise to some interesting complexity studies. Among them, we note the work of Hofbauer and Lautemann [6], who esta... |

38 | Higher-dimensional word problems with applications to equational logic
- Burroni
- 1993
(Show Context)
Citation Context ...and non-deterministic polynomial time functions. 1 Introduction Polygraphs are special higher-dimensional categories, introduced by Albert Burroni to provide a unified algebraic setting for rewriting =-=[3]-=-. For example, any term rewriting system can be translated into a polygraph which has, in case of left-linearity, exactly the same properties of termination and confluence [10, 6]. Here, we study how ... |

18 |
Termination proofs and the length of derivations
- Hofbauer, Lautemann
- 1989
(Show Context)
Citation Context ...g systems [9]. Let us recall that, in the term rewriting framework, polynomial interpretations gave rise to some interesting complexity studies. Among them, we note the work of Hofbauer and Lautemann =-=[6]-=-, who established a doubly exponential bound on the derivation length of systems with polynomial interpretations. We mention also the work of Cichon and Lescanne [4] who studied thes40 45 50 55 60 65 ... |

16 |
Polynomial interpretations and the complexity of algorithms
- Cichon, Lescanne
- 1992
(Show Context)
Citation Context ....bonfante@loria.fr. 2 yves.guiraud@loria.fr. 3 UMR 7503 CNRS – INPL – INRIA – UHP – Nancy 2.s2. Polygraphs as a computational model polynomial interpretations [13] cannot with the method described in =-=[4, 1]-=- or to give better bounds, as indicated here and in [8]. Moreover, the polygraphic interpretations give separated information on the spatial and on the temporal complexities of functions. Because of s... |

12 | Termination orders for 3-dimensional rewriting
- Guiraud
(Show Context)
Citation Context ...olynomial time and, going further, polynomial time functions. 1 Introduction Polygraphs provide a unified algebraic structure for rewriting systems, as intended by Burroni [3] and subsequently proved =-=[8, 5]-=-. Here we study how these mathematical objects can be used as a computational model. Roughly speaking, computations are done by a net of cells which individually behave according to some local transit... |

7 |
an algebraic theory of boolean circuits
- Towards
(Show Context)
Citation Context ...olynomial time and, going further, polynomial time functions. 1 Introduction Polygraphs provide a unified algebraic structure for rewriting systems, as intended by Burroni [3] and subsequently proved =-=[8, 5]-=-. Here we study how these mathematical objects can be used as a computational model. Roughly speaking, computations are done by a net of cells which individually behave according to some local transit... |

4 |
Hélène Touzet. Algorithms with polynomial interpretation termination proof
- Bonfante, Cichon, et al.
(Show Context)
Citation Context ...nd Lescanne [4] who studied thes40 45 50 55 60 65 2. Polygraphs as a computational model computational power of these systems and, finally, the work of Cichon, Marion and Touzet with the first author =-=[1]-=- who identified complexity classes by means of restrictions on polynomial interpretations. However, some new difficulties arise when considering polygraphs. For example, duplication and erasure are ex... |

4 |
Interaction nets, Principles of Programming Languages
- Lafont
- 1990
(Show Context)
Citation Context ..., computations are done by a net of cells which individually behave according to some local transition rules: this model is close to von Neumann’s cellular automata [10] and Lafont’s interaction nets =-=[7]-=-. While von Neumann’s automata are essentially synchronous, interaction nets and polygraphs are asynchronous. The difference between the last two models is that polygraphs have a much more rigid geome... |

2 |
Bonfante and Yves Guiraud, Programs as polygraphs: computability and complexity
- Guillaume
- 2006
(Show Context)
Citation Context ...s interpretation, we give a polynomial upper bound on the number of structural steps that will be performed. This document is an overview of ideas and results contained in a paper by the same authors =-=[2]-=-, containing more comments, technical details and all the proofs. 2 Polygraphs as a computational model The programs we consider are represented by rewriting systems on "algebraic circuits", consistin... |