Linear logic and permutation stacks—the Forth shall be first

Baker, Henry G.

doi:10.1145/181993.181999

Cited by 5 publications

(2 citation statements)

References 75 publications

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“…Before proceeding further it will be convenient to informally recall the definition of 'lattice gas' and the structural difference between cellular automata and lattice gases. The simplest nontrivial 3 LG have the format of Fig. 2.…”

Section: T T+1mentioning

confidence: 99%

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When–and how–can a cellular automaton be rewritten as a lattice gas?

Toffoli

Capobianco

Mentrasti

2008

Theoretical Computer Science

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a b s t r a c tBoth cellular automata (CA) and lattice-gas automata (LG) provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics; it is customary to use the terms 'cellular automaton' and 'lattice gas' for a dynamic system itself as well as for its presentation. The two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability.Following a conjecture by Toffoli and Margolus, it had been proved by Kari that any invertible CA, at least up to two dimensions, can be rewritten as an isomorphic LG. But until now it was not known whether this is possible in general for noninvertible CA-which comprise ''almost all'' CA and represent the bulk of examples in theory and applications. Even circumstantial evidence -whether in favor or against -was lacking.Here, for noninvertible CA, (a) we prove that an LG presentation is out of the question for the vanishingly small class of surjective ones. We then turn our attention to all the restnoninvertible and nonsurjective -which comprise all the typical ones, including Conway's 'Game of Life'. For these (b) we prove by explicit construction that all the one-dimensional ones are representable as LG, and (c) we present and motivate the conjecture that this result extends to any number of dimensions.The tradeoff between dissipation rate and structural complexity implied by the above results have compelling implications for the thermodynamics of computation at a microscopic scale.

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Section: T T+1mentioning

confidence: 99%

“…The no-fanout constraint is used with the same meaning, though in an independent line of research, in Girard's linear logic [15]. There, as here, multiple uses require explicit duplication, with all the costs (in infrastructure or running expenses) that that may entail (see also [3]).…”

Section: T T+1mentioning

confidence: 99%

When–and how–can a cellular automaton be rewritten as a lattice gas?

Toffoli

Capobianco

Mentrasti

2008

Theoretical Computer Science

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A Virtual Machine for Supporting Reversible Probabilistic Guarded Command Languages

Stoddart

Lynas

Zeyda

2010

Electronic Notes in Theoretical Computer Science

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The Boyer benchmark meets linear logic

Baker¹

1993

SIGPLAN Lisp Pointers

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Of the Gabriel Lisp Benchmarks, the Boyer Benchmark ("Boyer") is the most representative of real AI applications, because it performs Prolog-like rule-directed rewriting, and because it relies heavily on garbage collection (GC) for the recovery of storage. We investigated the notion that such programs are unsuitable for explicit storage management---e.g., by means of a "linear" programming style in which every bound name dynamically occurs exactly once. We programmed Boyer in a "linear" fragment of Lisp in both interpretive-rule and compiled-rule versions, using both true linear (unshared) and reference count methods.We found that since the intermediate result of rewrite is unshared, the linear interpreted version is slower than the non-linear interpreted version, while the linear compiled version is slightly faster than the non-linear compiled version. When sharing is allowed, requiring reference counts for the linear versions, the linear shared versions are not competitive with the non-linear versions, except when "anchored pointers" are used. The anchored pointer reference count version, which reclaims storage, is still 1.25X slower than the non-linear version, which reclaims no storage.

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Linear logic and permutation stacks—the Forth shall be first

Cited by 5 publications

References 75 publications

When–and how–can a cellular automaton be rewritten as a lattice gas?

When–and how–can a cellular automaton be rewritten as a lattice gas?

A Virtual Machine for Supporting Reversible Probabilistic Guarded Command Languages

The Boyer benchmark meets linear logic

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