Computing with Membranes (P Systems): Universality Results

Martı́n-Vide, Carlos; Păun, Gheorghe

doi:10.1007/3-540-45132-3_5

Cited by 8 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Computational Completeness: The ability to use P systems as models for computation can be seen as a fundamental aspect in the field of membrane computing [9]. Investigations about their (sub)classes of computability depending on certain combinations of system properties and restrictions motivate theoretically inspired contributions to the field.…”

Section: Determinismmentioning

confidence: 99%

A Protein Substructure Based P System for Description and Analysis of Cell Signalling Networks

2006

View full text Add to dashboard Cite

Abstract. The way how cell signals are generated, encoded, transferred, modified, and utilised is essential for understanding information processing inside living organisms. The tremendously growing biological knowledge about proteins and their interactions draws a more and more detailed image of a complex functional network. Considering signalling networks as computing devices, the detection of structural principles, especially modularisation into subunits and interfaces between them, can help to seize ideas for their description and analysis. Algebraic models like P systems prove to be appropriate to this. We utilise string-objects to carry information about protein binding domains and their ligands. Embedding these string-objects into a deterministic graph structured P system with dynamical behaviour, we introduce a model that can describe cell signalling pathways on a submolecular level. Beyond questions of formal languages, the model facilitates tracing the evolutionary development from single protein components towards functional interacting networks. We exemplify the model by means of the yeast pheromone pathway.

show abstract

Section: Determinismmentioning

confidence: 99%

A Protein Substructure Based P System for Description and Analysis of Cell Signalling Networks

2006

View full text Add to dashboard Cite

show abstract

“…sets. Notice that, for P systems that deal with symbol objects, proofs for universality almost always use the theoretical tool through matrix grammar with appearance checking [17]. Here, we employ a new tool using Diophantine equations.…”

Section: Presburger Reachability Of Non-cooperative Signaling Systemsmentioning

confidence: 99%

“…set (of integer tuples) is also Diophantine. We note that, for P systems that deal with symbol objects, proofs for universality almost always use the theoretical tool through matrix grammar with appearance checking [17] or through Minsky's two-counter machines. Here, we employ a new tool using Diophantine equations, which facilitates elegant proofs of the undecidable results.…”

Section: Introductionmentioning

confidence: 99%

Signaling P Systems and Verification Problems

Dang

Ibarra

et al. 2005

Automata, Languages and Programming

View full text Add to dashboard Cite

Abstract.We introduce a new model of membrane computing system (or P system), called signaling P system. It turns out that signaling systems are a form of P systems with promoters that have been studied earlier in the literature. However, unlike non-cooperative P systems with promoters, which are known to be universal, noncooperative signaling systems have decidable reachability properties. Our focus in this paper is on verification problems of signaling systems; i.e., algorithmic solutions to a verification query on whether a given signaling system satisfies some desired behavioral property. Such solutions not only help us understand the power of "maximal parallelism" in P systems but also would provide a way to validate a (signaling) P system in vitro through digital computers when the P system is intended to simulate living cells. We present decidable and undecidable properties of the model of non-cooperative signaling systems using proof techniques that we believe are new in the P system area. For the positive results, we use a form of "upper-closed sets" to serve as a symbolic representation for configuration sets of the system, and prove decidable symbolic modelchecking properties about them using backward reachability analysis. For the negative results, we use a reduction via the undecidability of Hilbert's Tenth Problem. This is in contrast to previous proofs of universality in P systems where almost always the reduction is via matrix grammar with appearance checking or through Minsky's two-counter machines. Here, we employ a new tool using Diophantine equations, which facilitates elegant proofs of the undecidable results. With multiplication being easily implemented under maximal parallelism, we feel that our new technique is of interest in its own right and might find additional applications in P systems.

show abstract

“…We believe that studying the computing power of P systems would lend itself to the discovery of new results if a similar methodology is followed. Indeed, much research work has shown that P systems and their many variants are universal (i.e., equivalent to TMs) [4,19,20,3,7,9,23] (surveys are found in [15,21,22]; see also the comprehensive bibliography at http://psystems.disco.unimib.it). However, there is little work in addressing the sub-Turing computing power of restricted P systems.…”

Section: Introductionmentioning

confidence: 99%

Catalytic P systems, semilinear sets, and vector addition systems

Ibarra

Dang

Eğecioǧlu

2004

Theoretical Computer Science

View full text Add to dashboard Cite

We look at 1-region membrane computing systems which only use rules of the form Ca → Cv, where C is a catalyst, a is a noncatalyst, and v is a (possibly null) string of noncatalysts. There are no rules of the form a → v. Thus, we can think of these systems as "purely" catalytic. We consider two types: (1) when the initial conÿguration contains only one catalyst, and (2) when the initial conÿguration contains multiple catalysts. We show that systems of the ÿrst type are equivalent to communication-free Petri nets, which are also equivalent to commutative context-free grammars. They deÿne precisely the semilinear sets. This partially answers an open question (in: WMC-CdeA'02, Computationally universal P systems without priorities: two catalysts are su cient, available at http://psystems. disco.unimib.it, 2003). Systems of the second type deÿne exactly the recursively enumerable sets of tuples (i.e., Turing machine computable). We also study an extended model where the rules are of the form q : (p; Ca → Cv) (where q and p are states), i.e., the application of the rules is guided by a ÿnite-state control. For this generalized model, type (1) as well as type (2) with some restriction correspond to vector addition systems. Finally, we brie y investigate the closure properties of catalytic systems.

show abstract

Computing with Membranes (P Systems): Universality Results

Cited by 8 publications

References 18 publications

A Protein Substructure Based P System for Description and Analysis of Cell Signalling Networks

A Protein Substructure Based P System for Description and Analysis of Cell Signalling Networks

Signaling P Systems and Verification Problems

Catalytic P systems, semilinear sets, and vector addition systems

Contact Info

Product

Resources

About