We present strategic port graph rewriting as a basis for the implementation of visual modelling tools. The goal is to facilitate the specification and programming tasks associated with the modelling of complex systems. A system is represented by an initial graph and a collection of graph rewrite rules, together with a user-defined strategy to control the application of rules. The traditional operators found in strategy languages for term rewriting have been adapted to deal with the more general setting of graph rewriting, and some new constructs have been included in the strategy language to deal with graph traversal and management of rewriting positions in the graph. We give a formal semantics for the language, and describe its implementation: the graph transformation and visualisation tool Porgy.

P systems with active membranes are a class of bioinspired computing models, where the rules are used in the non-deterministic maximally parallel manner. In this paper, first, a new variant of timed P systems with active membranes is proposed, where the application of rules can be regulated by promoters with only two polarizations. Next, we prove that any Turing computable set of numbers can be generated by such a P system in the time-free way. Moreover, we construct a uniform solution to the $\mathcal{SAT}$ problem in the framework of such recognizer timed P systems in polynomial time, and the feasibility and effectiveness of the proposed system is demonstrated by an instance. Compared with the existing methods, the P systems constructed in our work require fewer necessary resources and RS-steps, which show that the solution is effective to NP-complete problem.

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group on the collection of homogeneous languages of length n ∈ ℕ. One recovers the isothetic regions from (Haucourt 2017, to appear (online since October 2017)) by considering the alphabet of connected subsets of the space |G|, viz the geometric realization of a finite graph G. Factoring the geometric model of a conservative program amounts to parallelize it, and there exists an efficient factoring algorithm for isothetic regions. Yet, from the theoretical point of view, one wishes to go beyond the class of conservative programs, which implies relaxing the finiteness hypothesis on the graph G. Provided that the collections of n-dimensional isothetic regions over G (denoted by |G|) are co-unital distributive lattices, the prime decomposition of isothetic regions is given by an algorithm which is, unfortunately, very inefficient. Nevertheless, if the collections |G| satisfy the stronger property of being Boolean algebras, then the efficient factoring algorithm is available again. We relate the algebraic properties of the collections |G| to the geometric properties of the space |G|. On the way, the algebraic structure |G| is proven to be the universal tensor product, in the category of semilattices with zero, of n copies of the algebraic structure |G|.