Filters








59,048 Hits in 6.9 sec

Complexity Classes and Rewrite Systems with Polynomial Interpretation [chapter]

G. Bonfante, A. Cichon, J. Y Marion, H. Touzet
1999 Lecture Notes in Computer Science  
As a consequence, we also characterize the linear space computable functions.  ...  We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs.  ...  Computability & polynomial interpretation The term rewriting notations used throughout are based on [5] .  ... 
doi:10.1007/10703163_25 fatcat:o553kzsno5ejnjklzurd3ytoju

A term-rewriting characterization of PSPACE [article]

Naohi Eguchi
2012 arXiv   pre-print
Isabel Oitavem has introduced a term rewriting system (TRS) which captures the class FPS of polynomial-space computable functions. We propose an alternative TRS for FPS.  ...  It turns out that our characterization is relatively simple and suggests an uniform approach to the space-complexity.  ...  In particular, the introduction of the non-confluent TRS R N and the use of the innermost strategy are due to him or her. I would also like to thank my thesis advisor Prof.  ... 
arXiv:1201.0562v1 fatcat:usy5xxpebnco7mvti2exmlc6ya

A TERM-REWRITING CHARACTERIZATION OF PSPACE

N. Eguchi
2009 Proceedings of the 10th Asian Logic Conference  
Isabel Oitavem has introduced a term rewriting system (TRS) which captures the class FPS of polynomial-space computable functions. We propose an alternative TRS for FPS.  ...  It turns out that our characterization is relatively simple and suggests an uniform approach to the space-complexity.  ...  In 1, a term rewriting characterization of the class FPS of functions computed in polynomial space was given.  ... 
doi:10.1142/9789814293020_0004 fatcat:5pihyxqlwreyjja6ebodawiyei

Characterizing Languages by Normalization and Termination in String Rewriting [chapter]

Jeroen Ketema, Jakob Grue Simonsen
2012 Lecture Notes in Computer Science  
We recall the well-known result that any recursively enumerable set of strings can occur as the set of normalizing strings over a "small" alphabet if the rewriting system is allowed access to a "larger  ...  We characterize sets of strings using two central properties from rewriting: normalization and termination.  ...  If F is a class of functions of type Γ + −→ Γ + , we say that F is time-defined (resp. space-defined) by G if F is exactly the class of functions of type Γ + −→ Γ + that are computed by a multi-tape deterministic  ... 
doi:10.1007/978-3-642-31653-1_41 fatcat:c6ijtd4me5g7vflu7zygyiifq4

Page 482 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
Applying these functions noncompetitively provides in both cases a characterization of the context-free languages. Peter R. J.  ...  A tree pattern is a structured pattern known as a term in logic program- ming and term rewriting systems, and a tree pattern language is the set of all ground instances of a tree pattern.  ... 

Page 2054 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Summary: “In this paper we focus on the class of functions com- putable in deterministic polynomial space—Pspace. Our aim is to give a survey on implicit characterizations of Pspace.  ...  We move on to a geomet- ric characterization of the well-known communication complexity class C-PP in terms of half-space representations achieving a large margin.  ... 

Complexity Invariance of Real Interpretations [chapter]

Guillaume Bonfante, Florian Deloup
2010 Lecture Notes in Computer Science  
In the field of implicit computational complexity, we are considering in this paper the fruitful branch of interpretation methods.  ...  We show that, actually, polynomials over the reals benefit from some properties that allow their safe use for complexity. We illustrate this by two characterizations, one of PTIME and one of PSPACE.  ...  We prove that even without the existence of such a δ, the derivation height of a term t is bounded by t up to a polynomial. To save some space, we have omitted some proofs.  ... 
doi:10.1007/978-3-642-13562-0_14 fatcat:lx5cwdmezfahrcrbugrgoh6uoq

Page 6185 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
(F-PARIS11-RI) Complexity analysis of term-rewriting systems. Theoret. Comput. Sci. 67 (1989), no. 2-3, 261-282. From the introduction: “In a paper by Choppy, P. Lescanne and J.- L.  ...  Rémy [in Proceedings of the International Workshop on Program Construction (Bonas, 1980), 159-181, MacMillan, New York, 1983; per bibl.], the cost of a term is defined as the number of rewriting steps  ... 

Page 1304 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
2003b:68071 2003b:68071 68Q15 03D15 68Q42 Oitavem, Isabel (P-LISB; Lisbon) A term rewriting characterization of the functions computable in polynomial space. (English summary) Arch. Math.  ...  The aim of the present paper is to give a characterization of PSPACE via term rewriting systems.  ... 

Unary Resolution: Characterizing Ptime [chapter]

Clément Aubert, Marc Bagnol, Thomas Seiller
2016 Lecture Notes in Computer Science  
We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring (whose elements can be understood as logic programs or sets of rewriting  ...  rules over first-order terms), a construction stemming from an interactive interpretation of cut-elimination known as the geometry of interaction.  ...  (this interactive point of view on computation has proven crucial in characterizing logarithmic space computation [17] ).  ... 
doi:10.1007/978-3-662-49630-5_22 fatcat:44jk7rigrfaxplojjlzxshhveu

Higher-order interpretations and program complexity

Patrick Baillot, Ugo Dal Lago
2016 Information and Computation  
For that we consider the notion of simply-typed term rewriting systems [30], we define higher-order polynomial interpretations for them and give a criterion ensuring that a program can be executed in polynomial  ...  This fits in the area of implicit computational complexity, which aims at giving machine-free characterizations of complexity classes.  ...  Many different complexity classes have been characterized this way, from polynomial time to polynomial space, to exponential time to logarithmic space.  ... 
doi:10.1016/j.ic.2015.12.008 fatcat:dhl3e24oofe2fpd5b23auqmvga

Memoization for Unary Logic Programming: Characterizing PTIME [article]

Clément Aubert
2015 arXiv   pre-print
We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting  ...  More precisely, we study the restriction of this framework to terms (and logic programs, rewriting rules) using only unary symbols.  ...  point of view on computation has proven crucial in characterizing logarithmic space computation [11] .  ... 
arXiv:1501.05104v2 fatcat:272rdzkgdjay5dozgcfuotkwym

Implicit computation complexity in higher-order programming languages

U. Dal Lago
2022 Mathematical Structures in Computer Science  
This paper is meant to be a survey about implicit characterizations of complexity classes by fragments of higher-order programming languages, with a special focus on type systems and subsystems of linear  ...  Particular emphasis will be put on Martin Hofmann's contributions to the subject, which very much helped in shaping the field.  ...  This allows us to define a type system very much in the style of safe recursion. This, however, does not lead us to a characterization of the polynomial computable functions.  ... 
doi:10.1017/s0960129521000505 fatcat:hk5qsgft6ng2lersxh35nuht6a

Page 2579 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
Summary: “We first show that ground term-rewriting systems can be completed in a polynomial number of rewriting steps, if the appropriate data structure for terms is used.  ...  Such requirements are satisfied whenever in any reduction each recursive call to a function occurs in a term in a position such that the term is P increasing at that position, P being a property of terms  ... 

Sparsity optimized high order finite element functions for H(curl) on tetrahedra

Sven Beuchler, Veronika Pillwein, Sabine Zaglmayr
2013 Advances in Applied Mathematics  
In this paper we construct a basis for conforming high-order finite element discretizations of the function space H(curl) in 3 dimensions.  ...  A rewriting procedure is used to explicitly evaluate the inner products. The precomputed matrix entries in this general form for the cell-based basis functions are available online.  ...  Acknowledgments This work has been supported by the FWF-projects P20121-N12, P20162-N18, P23484-N18, and the doctoral program "Computational Mathematics" (W1214).  ... 
doi:10.1016/j.aam.2012.11.004 fatcat:c5swi3cqw5bd5e3trqcniqym2m
« Previous Showing results 1 — 15 out of 59,048 results