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Complexity Classes and Rewrite Systems with Polynomial Interpretation
[chapter]

1999
*
Lecture Notes in Computer Science
*

As

doi:10.1007/10703163_25
fatcat:o553kzsno5ejnjklzurd3ytoju
*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] . ...##
###
A term-rewriting characterization of PSPACE
[article]

2012
*
arXiv
*
pre-print

Isabel Oitavem has introduced

arXiv:1201.0562v1
fatcat:usy5xxpebnco7mvti2exmlc6ya
*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. ...##
###
A TERM-REWRITING CHARACTERIZATION OF PSPACE

2009
*
Proceedings of the 10th Asian Logic Conference
*

Isabel Oitavem has introduced

doi:10.1142/9789814293020_0004
fatcat:5pihyxqlwreyjja6ebodawiyei
*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. ...##
###
Characterizing Languages by Normalization and Termination in String Rewriting
[chapter]

2012
*
Lecture Notes in Computer Science
*

We recall

doi:10.1007/978-3-642-31653-1_41
fatcat:c6ijtd4me5g7vflu7zygyiifq4
*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 ...##
###
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]

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. ...

##
###
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]

2016
*
Lecture Notes in Computer Science
*

We give

doi:10.1007/978-3-662-49630-5_22
fatcat:44jk7rigrfaxplojjlzxshhveu
*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] ). ...##
###
Higher-order interpretations and program complexity

2016
*
Information and Computation
*

For that we consider

doi:10.1016/j.ic.2015.12.008
fatcat:dhl3e24oofe2fpd5b23auqmvga
*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*. ...##
###
Memoization for Unary Logic Programming: Characterizing PTIME
[article]

2015
*
arXiv
*
pre-print

We give

arXiv:1501.05104v2
fatcat:272rdzkgdjay5dozgcfuotkwym
*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] . ...##
###
Implicit computation complexity in higher-order programming languages

2022
*
Mathematical Structures in Computer Science
*

This paper is meant to be

doi:10.1017/s0960129521000505
fatcat:hk5qsgft6ng2lersxh35nuht6a
*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*. ...##
###
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

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). ...

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