Graph Transformation

doi:10.1007/978-3-030-51372-6

Cited by 6 publications

(42 citation statements)

References 19 publications

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“…Throughout this paper, we will consider categorical rewriting theories over categories that satisfy the following sets of properties (with DPO-and SqPO-semantics to be introduced below) 1 : Assumption 1 (cf. [7], As. 1).…”

Section: Dpo-and Sqpo-type Compositional Rewriting Semanticsmentioning

confidence: 99%

“…The methodology developed in the present paper relies heavily upon the mathematical formalism introduced in [2,3,9,4,7,10], yet due to space restrictions, we will only provide some notations and essential definitions here, inviting the interested readers to consult loc. cit.…”

Section: Prerequisite: the Rule Algebra Frameworkmentioning

confidence: 99%

“…Referring yet again to [6,7] for the full technical details, suffice it here to quote the essential definitions: Definition 6 (Rule algebras; [7], Def. 5).…”

Section: Dpo-and Sqpo-type Rule Algebra Frameworkmentioning

confidence: 99%

“…We refer to R T C := (R C , T ) as the T-type rule algebra over C. Definition 7 (Representations; [7], Def. 6).…”

Section: Dpo-and Sqpo-type Rule Algebra Frameworkmentioning

confidence: 99%

“…The remedy for the aforementioned conceptual problem is the introduction of the concept of pattern count observables. Referring to [7] for the precise derivation, depending on the rewriting semantics T ∈ {DPO, SqPO} utilized, let us introduce the following definitions:…”

Section: Pattern Count Observablesmentioning

confidence: 99%

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On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

Behr

2021

Electron. Proc. Theor. Comput. Sci.

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Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and certain types of generating function expressions in combinatorics. We introduce a number of generating function techniques that permit a novel form of static analysis for rewriting systems based upon marginalizing distributions over the states of the rewriting systems via pattern-counting observables. * The author would like to thank Paul-André Melliès and Noam Zeilberger for fruitful discussions and valuable feedback. 1 We invite the readers to consult [6] or [7] for compact accounts of the relevant technical definitions of M-adhesive categories, pullbacks, pushouts, pushout complements, final pullback complements and their respective properties.

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Section: Dpo-and Sqpo-type Compositional Rewriting Semanticsmentioning

confidence: 99%

Section: Prerequisite: the Rule Algebra Frameworkmentioning

confidence: 99%

“…Referring yet again to [6,7] for the full technical details, suffice it here to quote the essential definitions: Definition 6 (Rule algebras; [7], Def. 5).…”

Section: Dpo-and Sqpo-type Rule Algebra Frameworkmentioning

confidence: 99%

“…We refer to R T C := (R C , T ) as the T-type rule algebra over C. Definition 7 (Representations; [7], Def. 6).…”

Section: Dpo-and Sqpo-type Rule Algebra Frameworkmentioning

confidence: 99%

Section: Pattern Count Observablesmentioning

confidence: 99%

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On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

Behr

2021

Electron. Proc. Theor. Comput. Sci.

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Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

Behr

Krivine

2020

Lecture Notes in Computer Science

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The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting theoretical methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds,. . .). In this paper, we contribute to the theoretical foundations of these types of rewriting theory a number of conceptual and technical developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double-and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics.

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Powerful and NP-Complete: Hypergraph Lambek Grammars

Pshenitsyn

2021

Graph Transformation

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Hypergraph Lambek grammars (HL-grammars) is a novel logical approach to generating graph languages based on the hypergraph Lambek calculus. In this paper, we establish a precise relation between HL-grammars and hypergraph grammars based on the double pushout (DPO) approach: we prove that HL-grammars generate the same class of languages as DPO grammars with the linear restriction on lengths of derivations. This can be viewed as a complete description of the expressive power of HL-grammars and also as an analogue of the Pentus theorem, which states that Lambek grammars generate the same class of languages as context-free grammars. As a corollary, we prove that HL-grammars subsume contextual hyperedge replacement grammars.

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Graph Transformation

Cited by 6 publications

References 19 publications

On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

Powerful and NP-Complete: Hypergraph Lambek Grammars

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