Ramified recurrence and computational complexity II: Substitution and poly-space

Leivant, Daniel; Marion, Jean-Yves

doi:10.1007/bfb0022277

Cited by 57 publications

(48 citation statements)

References 26 publications

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“…However, in the general setting, this notion of working space is meaningless, as pointed in [Mic89]: on some structures like (R, 0, 1, =, +, −, * ), any computation can be done in constant working space. However, since we have in the classical setting PAR = PSPACE, our result extends the classical one from [LM95].…”

Section: Simulation Of a P-uniform Family Of Circuitssupporting

confidence: 65%

“…As shown in the simulation of a BSS machine by safe recursive functions, we need to have a simultaneous recursion able to define simultaneously three functions in order to prove Theorem 2. In the classical setting, this is the choice made by Leivant and Marion in [LM95], while Bellantoni and cook used a smash function # to build and break t-uples [BC92]. Both choices are equivalent.…”

Section: Containing the Basic Safe Functions And Closed Under The Opmentioning

confidence: 99%

“…In the classical setting (see [LM95]), safe recursion with substitution characterizes the class PSPACE. However, in the general setting, this notion of working space is meaningless, as pointed in [Mic89]: on some structures like (R, 0, 1, =, +, −, * ), any computation can be done in constant working space.…”

Section: Simulation Of a P-uniform Family Of Circuitsmentioning

confidence: 99%

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Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Bournez

Cucker

Naurois

et al. 2003

Lecture Notes in Computer Science

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Abstract. We provide several machine-independent characterizations of deterministic complexity classes in the model of computation proposed by L. Blum, M. Shub and S. Smale. We provide a characterization of partial recursive functions over any arbitrary structure. We show that polynomial time computable functions over any arbitrary structure can be characterized in term of safe recursive functions. We show that polynomial parallel time decision problems over any arbitrary structure can be characterized in terms of safe recursive functions with substitutions.

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Section: Simulation Of a P-uniform Family Of Circuitssupporting

confidence: 65%

Section: Containing the Basic Safe Functions And Closed Under The Opmentioning

confidence: 99%

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Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Bournez

Cucker

Naurois

et al. 2003

Lecture Notes in Computer Science

Self Cite

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“…To the author's knowledge, all the other charaterization results are novel. Similar results can be ascribed to Leivant and Marion [25,22], but they do not take linearity constraints into account. Notice that, in presence of ramification, going from W to A dramatically increases the expressive power, while going from W to ∅ does not cause any loss of expressivity.…”

Section: Subsystemssupporting

confidence: 66%

The geometry of linear higher-order recursion

Lago

2009

ACM Trans. Comput. Logic

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“…In a previous paper [5], based on classical characterizations in [3] and [19], we exhibited machine-independent characterizations of the classes of functions over an arbitrary structure computable in polynomial sequential or parallel time. Our aim here is to provide such machine-independent characterizations over an arbitrary structure for polynomial hierarchy and polynomial alternating time.…”

Section: Introductionmentioning

confidence: 99%

Tailoring Recursion to Characterize Non-Deterministic Complexity Classes Over Arbitrary Structures

Bournez

Cucker

Naurois

et al. 2004

IFIP International Federation for Information Processing

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We provide machine-independent characterizations of some complexity classes, over an arbitrary structure, in the model of computation proposed by L. Blum, M. Shub and S. Smale. We show that the levels of the polynomial hierarchy correspond to safe recursion with predicative minimization. The levels of the digital polynomial hierarchy correspond to safe recursion with digital predicative minimization. Also, we show that polynomial alternating time corresponds to safe recursion with predicative substitutions and that digital polynomial alternating time corresponds to safe recursion with digital predicative substitutions.

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Ramified recurrence and computational complexity II: Substitution and poly-space

Cited by 57 publications

References 26 publications

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

The geometry of linear higher-order recursion

Tailoring Recursion to Characterize Non-Deterministic Complexity Classes Over Arbitrary Structures

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