85 research outputs found
GSOS for non-deterministic processes with quantitative aspects
Recently, some general frameworks have been proposed as unifying theories for
processes combining non-determinism with quantitative aspects (such as
probabilistic or stochastically timed executions), aiming to provide general
results and tools. This paper provides two contributions in this respect.
First, we present a general GSOS specification format (and a corresponding
notion of bisimulation) for non-deterministic processes with quantitative
aspects. These specifications define labelled transition systems according to
the ULTraS model, an extension of the usual LTSs where the transition relation
associates any source state and transition label with state reachability weight
functions (like, e.g., probability distributions). This format, hence called
Weight Function SOS (WFSOS), covers many known systems and their bisimulations
(e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS,
Segala-GSOS, among others).
The second contribution is a characterization of these systems as coalgebras
of a class of functors, parametric on the weight structure. This result allows
us to prove soundness of the WFSOS specification format, and that
bisimilarities induced by these specifications are always congruences.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Distributive Laws for Monotone Specifications
Turi and Plotkin introduced an elegant approach to structural operational
semantics based on universal coalgebra, parametric in the type of syntax and
the type of behaviour. Their framework includes abstract GSOS, a categorical
generalisation of the classical GSOS rule format, as well as its categorical
dual, coGSOS. Both formats are well behaved, in the sense that each
specification has a unique model on which behavioural equivalence is a
congruence. Unfortunately, the combination of the two formats does not feature
these desirable properties. We show that monotone specifications - that
disallow negative premises - do induce a canonical distributive law of a monad
over a comonad, and therefore a unique, compositional interpretation.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004
Bialgebraic Semantics for Logic Programming
Bialgebrae provide an abstract framework encompassing the semantics of
different kinds of computational models. In this paper we propose a bialgebraic
approach to the semantics of logic programming. Our methodology is to study
logic programs as reactive systems and exploit abstract techniques developed in
that setting. First we use saturation to model the operational semantics of
logic programs as coalgebrae on presheaves. Then, we make explicit the
underlying algebraic structure by using bialgebrae on presheaves. The resulting
semantics turns out to be compositional with respect to conjunction and term
substitution. Also, it encodes a parallel model of computation, whose soundness
is guaranteed by a built-in notion of synchronisation between different
threads
Bialgebraic Semantics for String Diagrams
Turi and Plotkin's bialgebraic semantics is an abstract approach to
specifying the operational semantics of a system, by means of a distributive
law between its syntax (encoded as a monad) and its dynamics (an endofunctor).
This setup is instrumental in showing that a semantic specification (a
coalgebra) satisfies desirable properties: in particular, that it is
compositional.
In this work, we use the bialgebraic approach to derive well-behaved
structural operational semantics of string diagrams, a graphical syntax that is
increasingly used in the study of interacting systems across different
disciplines. Our analysis relies on representing the two-dimensional operations
underlying string diagrams in various categories as a monad, and their
bialgebraic semantics in terms of a distributive law over that monad.
As a proof of concept, we provide bialgebraic compositional semantics for a
versatile string diagrammatic language which has been used to model both signal
flow graphs (control theory) and Petri nets (concurrency theory). Moreover, our
approach reveals a correspondence between two different interpretations of the
Frobenius equations on string diagrams and two synchronisation mechanisms for
processes, \`a la Hoare and \`a la Milner.Comment: Accepted for publications in the proceedings of the 30th
International Conference on Concurrency Theory (CONCUR 2019
Structural operational semantics for stochastic and weighted transition systems
We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature
Presenting Distributive Laws
Distributive laws of a monad T over a functor F are categorical tools for
specifying algebra-coalgebra interaction. They proved to be important for
solving systems of corecursive equations, for the specification of well-behaved
structural operational semantics and, more recently, also for enhancements of
the bisimulation proof method. If T is a free monad, then such distributive
laws correspond to simple natural transformations. However, when T is not free
it can be rather difficult to prove the defining axioms of a distributive law.
In this paper we describe how to obtain a distributive law for a monad with an
equational presentation from a distributive law for the underlying free monad.
We apply this result to show the equivalence between two different
representations of context-free languages
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