The chemical abstract machine

Berry, Gérard; Boudol, Gérard

doi:10.1016/0304-3975(92)90185-i

Cited by 673 publications

(265 citation statements)

References 10 publications

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“…where it was shown that a Turing machine could be simulated by a chemical reaction network with a small probability of error. Although not surprising, this result is in sharp contrast to the discrete semantics of reaction systems which are not Turing complete without either the tolerance of a small probability error [17], or the addition of other mechanisms such as the unbounded dynamic creation of membranes [2,38,9], or the presence of polymerization reactions on an infinite universe of polymers [10] or DNA stacks [40].…”

Section: Definition 2 ([48])mentioning

confidence: 81%

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

Fages

Guludec

Bournez

et al. 2017

Computational Methods in Systems Biology

100

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Abstract. When seeking to understand how computation is carried out in the cell to maintain itself in its environment, process signals and make decisions, the continuous nature of protein interaction processes forces us to consider also analog computation models and mixed analog-digital computation programs. However, recent results in the theory of analog computability and complexity establish fundamental links with classical programming. In this paper, we derive from these results the strong (uniform computability) Turing completeness of chemical reaction networks over a finite set of molecular species under the differential semantics, solving a long standing open problem. Furthermore we derive from the proof a compiler of mathematical functions into elementary chemical reactions. We illustrate the reaction code generated by our compiler on trigonometric functions, and on various sigmoid functions which can serve as markers of presence or absence for implementing program control instructions in the cell and imperative programs. Then we start comparing our compiler-generated circuits to the natural circuit of the MAPK signaling network, which plays the role of an analog-digital converter in the cell with a Hill type sigmoid input/output functions.

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Section: Definition 2 ([48])mentioning

confidence: 81%

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

Fages

Guludec

Bournez

et al. 2017

Computational Methods in Systems Biology

100

View full text Add to dashboard Cite

show abstract

“…This is factored into two parts, in the style of [BB90]: a structural congruence ≡ and a reduction relation →.…”

Section: Linear Realizability Algebramentioning

confidence: 99%

Proof Nets as Formal Feynman Diagrams

Blute

Panangaden

2010

New Structures for Physics

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Summary. The introduction of linear logic and its associated proof theory has revolutionized many semantical investigations, for example, the search for fullyabstract models of PCF and the analysis of optimal reduction strategies for lambda calculi. In the present paper we show how proof nets, a graph-theoretic syntax for linear logic proofs, can be interpreted as operators in a simple calculus. This calculus was inspired by Feynman diagrams in quantum field theory and is accordingly called the φ-calculus. The ingredients are formal integrals, formal power series, a derivative-like construct and analogues of the Dirac delta function.Many of the manipulations of proof nets can be understood as manipulations of formulas reminiscent of a beginning calculus course. In particular, the "box" construct behaves like an exponential and the nesting of boxes phenomenon is the analogue of an exponentiated derivative formula. We show that the equations for the multiplicative-exponential fragment of linear logic hold.

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“…Multisets of nested nodes -There have been many diverse proposals of computational models equipped with the notion of multisets, early examples of which include Petri Nets and Production Systems. Concurrent processes naturally form multisets; Gamma [2] and Chemical Abstract Machines [3] are two typical computational models based on multiset rewriting; languages based on Linear Logic [10] take advantage of the fact that the both sides of a sequent are multisets; Linda's tuple spaces are multisets of tuples.…”

Section: Overview Of Lmntal and Related Workmentioning

confidence: 99%

LMNtal: A Language Model with Links and Membranes

Ueda

Kato

2005

Membrane Computing

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LMNtal (pronounced "elemental ") is a simple language model based on graph rewriting that uses logical variables to represent links and membranes to represent hierarchies. The two major goals of LMNtal are (i) to unify various computational models based on multiset rewriting and (ii) to serve as the basis of a truly general-purpose language covering various platforms ranging from wide-area to embedded computation. Another important contribution of the model is it greatly facilitates programming with dynamic data structures.

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The chemical abstract machine

Cited by 673 publications

References 10 publications

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

Proof Nets as Formal Feynman Diagrams

LMNtal: A Language Model with Links and Membranes

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