Logspace without Bounds

Oitavem, Isabel

doi:10.1515/9783110324907.355

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…ramified recurrence has been used to obtain machine-independent characterizations of several major complexity classes, such as polynomial time [4,22] and polynomial space [26,36], as well as alternating log time [8,27], alternating poly-log time [8], NC [23,35], logarithmic space [34], monotonic PTime [13], linear space [21,15,22], NP [2,37], the poly-time hierarchy [3], exponential time [10], Kalmarelementary resources [24], and probabilistic polynomial time [20]. The method is all the more of interest given the roots of ramification in the foundations of mathematics [42,41], thus bridging abstraction levels in set-theory and type-theory to computational complexity classes.…”

Section: The Ramification Methodsmentioning

confidence: 99%

A generic imperative language for polynomial time

Leivant

2019

Preprint

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We propose a generic imperative programming language STR that captures PTime computations, on both infinite inductive structures and families of finite structures. The approach, set up in [29] for primitive-recursive complexity, construes finite partial-functions as a universal canonical form of data, and uses structure components for loop variants. STR is obtained by the further refinement that assigns ranks to finite partial-functions, which regulate the interaction of loops, yielding programs that run in polynomial time.STR captures algorithms that have eluded ramified recurrence, and is promising as an artifact of Implicit Complexity which is malleable to static analysis implementations.

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Section: The Ramification Methodsmentioning

confidence: 99%

A generic imperative language for polynomial time

Leivant

2019

Preprint

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“…The work in this paper builds on earlier work on implicit characterisations of logarithmic space complexity classes. While implicit characterisations of complexity classes often focus on minimal formal systems, such as function algebras [36,38,39] or while-languages [26], the results are useful in obtaining a better understanding of the resource usage properties of programming languages. Bonfante [8] shows how to capture logspace by a firstorder functional language.…”

Section: Implicit Characterisations Of Logarithmic Spacementioning

confidence: 99%

Computation by interaction for space-bounded functional programming

Lago

Schöpp

2016

Information and Computation

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We consider the problem of supporting sublinear space programming in a functional programming language. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot compose functions directly for lack of space for the intermediate result, but must instead compute and recompute small parts of the intermediate result on demand. In this paper, we study how the implementation of such techniques can be supported by functional programming languages. Our approach is based on modelling computation by interaction using the Int construction of Joyal, Street & Verity. We derive functional programming constructs from the structure obtained by applying the Int construction to a term model of a given functional language. The thus derived core functional language intml is formulated by means of a type system inspired by Baillot & Terui's Dual Light Affine Logic. It can be understood as a programming language simplification of Stratified Bounded Affine Logic. We show that it captures the classes flogspace and nflogspace of the functions computable in deterministic logarithmic space and in non-deterministic logarithmic space, respectively. We illustrate the expressiveness of intml by showing how typical graph algorithms, such a test for acyclicity in undirected graphs, can be represented in it.

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Logspace without Bounds

Cited by 2 publications

References 14 publications

A generic imperative language for polynomial time

A generic imperative language for polynomial time

Computation by interaction for space-bounded functional programming

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