pdf/restriction-categories-i-categories-of-partial-maps-3azyzl662g.pdf

Restriction categories I: categories of partial maps

A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split Restriction categories facilitate reasoning about partial maps as they have a purely algebraic formulation 
In this paper we consider colimits and limits in restriction categories As the notion of restriction category is not self-dual, we should not expect colimits and limits in restriction categories to behave in the same manner The notion of colimit in the restriction context is quite straightforward, but limits are more delicate The suitable notion of limit turns out to be a kind of lax limit, satisfying certain extra properties 
Of particular interest is the behaviour of the coproduct both by itself and with respect to partial products We explore various conditions under which the coproducts are ``extensive'' in the sense that the total category (of the related partial map category) becomes an extensive category When partial limits are present, they become ordinary limits in the total category Thus, when the coproducts are extensive we obtain as the total category a lextensive category This provides, in particular, a description of the extensive completion of a distributive category

Restriction categories III: colimits, partial limits, and extensivity

We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.

http://www.lacl.fr/~michel/PUBLIS/2008/biosystem08.pdf

Stochastic P systems and the simulation of biochemical processes with dynamic compartments

In this paper we present a theory of computational complexity in the framework of membrane computing. Polynomial complexity classes in recognizer membrane systems and capturing the classical deterministic and non-deterministic modes of computation, are introduced. In this context, a characterization of the relation P=NP is described.

An approach to computational complexity in membrane computing

/pdf/substitution-up-to-isomorphism-jndzsdkobq.pdf

Substitution up to isomorphism

Presentation equationnelle des categories de morphismes partiels avec etablissement systematique des rapports entre ces structures et les classiques structures totales

Partiality, cartesian closedness, and toposes

The aim of this paper is to (preliminarily) discuss various ways of introducing probabilities in membrane systems. We briefly present both ideas already circulated in the literature and new proposals, trying to have a systematic overview of possibilities of associating probabilities with the ingredients of a membrane system: with (localization of) single objects, with multiplicities of objects (hence with the multisets), with the rules (depending or not on the previous applied rule), with the communication targets. For a certain mode of using the probabilities associated with the evolution rules (in string-object P systems) we obtain the computational universality.

In search of) probabilistic P systems

There are introduced and discussed stochastic and randomized P systems. Stochastic P systems are aimed to describe distortions which may appear in evolution processes of membrane systems considered in the area of membrane computing. Randomized P systems serve for implementation of randomized algorithms. There is presented a family of randomized P systems which serve for implementation of Miller-Rabin randomized algorithm for primality of integers. P systems of this family verify primality of integers in a polynomial time, with a low error probability, and with a subexponential number of processors modelled as membranes with evolving contents.

Probabilistic P Systems

We investigate the three classes of accepting P systems considered so far, namely the P automata of Csuhaj-Varju, Vaszil [3], their variant introduced by Madhu, Krithivasan [10], and the related machinery of Freund, Oswald [5]. All three variants of automata-like P systems are based on symport/antiport rules. For slight variants of the first two classes we prove that any recursively enumerable language can be recognized by systems with only two membranes (this considerably improves the result from [3], where systems with seven membranes were proved to be universal). We also introduce the initial mode of accepting strings (the strings are introduced into the system, symbol by symbol, at the beginning of a computation), and we briefly investigate this mode for the three classes of automata, especially for languages over a one-letter alphabet. Some open problems are formulated, too.

On three classes of automata-like P systems

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Partiality, cartesian closedness, and toposes

In search of) probabilistic P systems

Probabilistic P Systems

On three classes of automata-like P systems

On three classes of automata-like P systems