Unexpected universality results for three classes of P systems with symport/antiport

Symport and antiport are biological ways of transporting molecules through membranesin ``collaborating' pairs; in the case of symport the two molecules pass in the same direction, in the case of antiport the two molecules pass in opposite directions. Here we first survey the results about the computing power of membrane systems (P systems) using only symport/antiport rules (hence these systems compute by communication only), then we consider a recently introduced, way of defining the result of a computation in a membrane system: looking for the trace of certain objects in their movement through membranes. Rather unexpected, in this way we get characterizations of recursively enumerable languages by means of membrane systems with symport/antiport which work with multisets of objects (note the qualitative difference between the data structure used by computations – multisets: no ordering– and the data structure of the output – strings: linear ordering). A similar remark holds true for the case of analysing P systems, which work in an automata-like manner: the sequence of certain distinguished objects taken from the environment during acomputation is the string recognized by the computation. We also survey universality results from this area, with sketched proofs. Some open problems are also formulated. This revised version was published online in June 2006 with corrections to the Cover Date.     

P systems with symport/antiport simulating counter automata

The generative capability of several variants of P systems with symport/antiport is studied via the simulation of counter automata. This leads to the reduction of the complexity, expressed in number of membranes and weight of rules, of P systems generating recursively enumerable sets.Received: 4 December 2003, Published online: 3 November 2004     

P systems with minimal parallelism

A current research topic in membrane computing is to find more realistic P systems from a biological point of view, and one target in this respect is to relax the condition of using the rules in a maximally parallel way. We contribute in this paper to this issue by considering the minimal parallelism of using the rules: if at least a rule from a set of rules associated with a membrane or a region can be used, then at least one rule from that membrane or region must be used, without any other restriction (e.g., more rules can be used, but we do not care how many). Weak as it might look, this minimal parallelism still leads to universality. We first prove this for the case of symport/antiport rules. The result is obtained both for generating and accepting P systems, in the latter case also for systems working deterministically. Then, we consider P systems with active membranes, and again the usual results are obtained: universality and the possibility to solve NP-complete problems in polynomial time (by trading space for time).     

Characterizations of context-sensitive languages and other language classes in terms of symport/antiport P systems

We give “syntactic’’ characterizations of context-sensitive languages (CSLs) in terms of some restricted models of symport/antiport P systems. These are the first such characterizations of CSLs in terms of P systems. In particular, we show the following for any language L over a binary alphabet:

(1)

Let m   be any integer ≥1$\ge 1$. Then L is a CSL if and only if it can be accepted by a restricted symport/antiport P system with m membranes and multiple number of symbols (objects). Moreover, holding the number of membranes at m, there is an infinite hierarchy in computational power (within the class of binary CSLs) with respect to the number of symbols.     

Efficient simulation of tissue-like P systems by transition cell-like P systems

In the framework of P systems, it is known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP-complete problems. Nonetheless, it could be sufficient to create an exponential number of membranes in polynomial time. Working with P systems whose membrane structure does not increase in size, it is known that it is not possible to solve computationally hard problems (unless P = NP), basically due to the impossibility of constructing exponential number of membranes, in polynomial time, using only evolution, communication and dissolution rules. In this paper we show how a family of recognizer tissue P systems with symport/antiport rules which solves a decision problem can be efficiently simulated by a family of basic recognizer P systems solving the same problem. This simulation allows us to transfer the result about the limitations in computational power, from the model of basic cell-like P systems to this kind of tissue-like P systems.     

Results on catalytic and evolution-communication P systems

In this paper we give several improved universality results for two important classes of P systems: P systems with catalysts and evolution-communication P systems. First, the result from Reference,¹⁴⁾ stating that six catalysts ensure the universality, has been improved in two ways: using bistable catalysts and using moving catalysts. Specifically, the universality can be reached with one bistable catalyst and 2 usual catalysts (using five membranes), as well as with one moving catalyst and three membranes, or with two moving catalysts and only two membranes. The second part of the paper deals with evolution-communication P systems, and we also give improved universality results for this type of systems, in terms of the weight of symport/antiport rules, number of membranes, or number of catalysts. Shankara Narayanan Krishna: She is an Assistant Professor in Dept. Computer Science & Engg, IIT Bombay, India. Her research interests are Natural Computing and Formal Methods. Andrei Paun, Ph.D.: He obtained his bachelor degree in Mathematics and Computer Science from the University of Bucharest, Romania. He obtaind his Ph.D. degree in Computer Science, at University of Western Ontario, Canada, under the supervision of Prof. Dr. Sheng Yu, with the thesis “Unconventional Models of Computation: DNA and Membrane Computing”. After graduation he received a postdoctoral felloship from NSERC, Canada and after six months he accepted an assistant professor position in US at Louisiana Tech University.     

Minimizing evolution-communication P systems and automata

Evolution-communication P systems are a variant of P systems allowing both rewriting rules and symport/antiport rules, thus having separated the rewriting and the communication. The purpose of this paper is to solve an open problem stated in Reference,¹⁾ namely generating the family of Turing computable sets of vectors of natural numbers instead of the family of Turing computable sets of natural numbers. The same construction also reduces the 3-membrane non-cooperative case and the 2-membrane 1-catalyst case to the 2-membrane non-cooperative case. Also, EC P automata are introduced and it is proved that 2-membrane EC P automata with a promoter can accept all recursively enumerable languages. Finally, a definition of an extended system is given, and its universality is proved using the rules of more restricted types. Artiom Alhazov: He has graduated from Mathematics and Computer Science, State University of Moldova in 2001, and is currently a Ph.D. student in Chişinăm, Moldova, and Tarragona, Spain. He has won prizes at 3 National Olympiads in Informatics and in Mathematics (1995 and 1996), participated at 8th International Olympiad in Informatics (Veszprem, Hungary, 1996). He has experience in programming and teaching, and has published 18 papers, mostly in Membrane Computing. His interests are Origami, Mathematics, Programming, Theoretical Computer Science, Formal Linguistics and Biocomputing.     

Tissue P systems with channel states

We consider tissue-like P systems with states associated with the links (we call them synapses) between cells, controlling the passage of objects across the links. We investigate the computing power of such devices for the case of using—in a sequential manner—antiport rules of small weights. Systems with two cells are proved to be universal when having arbitrarily many states and minimal antiport rules, or one state and antiport rules of weight two. Also the systems with arbitrarily many cells, three states, and minimal antiport rules are universal. In contrast, the systems with one cell and any number of states and rules of any weight only compute Parikh sets of matrix languages (generated by matrix grammars without appearance checking); characterizations of Parikh images of matrix languages are obtained for such one-cell systems with antiport rules of a reduced weight.     

One-membrane symport with few extra symbols

Membrane systems (with symbol objects) are formal models of distributed parallel multiset processing. Symport rules move multiple objects to a neighbouring region. It is known that for P systems with symport rules of weight at most 3 and a single membrane, seven superfluous symbols are enough for computational completeness, and one is necessary. We present the improvements of the lower bounds on the generative power of P systems with symport of weight bounded by 3 and 4, in particular, establishing that six and two extra symbols suffice, respectively. Besides maximally parallel P systems, we also consider sequential ones. In fact, all presented non-universality lower bound results, together with all upper bound results, hold also in this case, yielding the current state of the art.     

Compositional semantics and behavioral equivalences for P Systems

The aim of the paper is to give a compositional semantics in the style of the Structural Operational Semantics (SOS) and to study behavioral equivalence notions for P Systems. Firstly, we consider P Systems with maximal parallelism and without priorities. We define a process algebra, called P Algebra, whose terms model membranes, we equip the algebra with a Labeled Transition System (LTS) obtained through SOS transition rules, and we study how some equivalence notions defined over the LTS model apply in our case. Then, we consider P Systems with priorities and extend the introduced framework to deal with them. We prove that our compositional semantics reflects correctly maximal parallelism and priorities.     

Scalable heterogeneous parallelism for atmospheric modeling and simulation

Heterogeneous multicore chipsets with many levels of parallelism are becoming increasingly common in high-performance computing systems. Effective use of parallelism in these new chipsets constitutes the challenge facing a new generation of large scale scientific computing applications. This study examines methods for improving the performance of two-dimensional and three-dimensional atmospheric constituent transport simulation on the Cell Broadband Engine Architecture (CBEA). A function offloading approach is used in a 2D transport module, and a vector stream processing approach is used in a 3D transport module. Two methods for transferring incontiguous data between main memory and accelerator local storage are compared. By leveraging the heterogeneous parallelism of the CBEA, the 3D transport module achieves performance comparable to two nodes of an IBM BlueGene/P, or eight Intel Xeon cores, on a single PowerXCell 8i chip. Module performance on two CBEA systems, an IBM BlueGene/P, and an eight-core shared-memory Intel Xeon workstation are given.     

ON THE OPTIMALITY OF ALLEN AND KENNEDY'S ALGORITHM FOR PARALLELISM EXTRACTION IN NESTED LOOPS

We explore the link between dependence abstractions and maximal parallelism extraction in nested loops. Our goal is to find, for each dependence abstraction, the minimal transformations needed for maximal parallelism extraction. The result of this paper is that Allen and Kennedy's algorithm is optimal when dependences are approximated by dependence levels. This means that even the most sophisticated algorithm cannot detect more parallelism than found by Allen and Kennedy's algorithm, as long as dependence level is the only information available. In other words, loop distribution is sufficient for detecting maximal parallelism in dependence graphs with levels.     

带膜分裂和促进剂的通讯膜系统求解QSAT问题

膜计算是自然计算的一个分支,膜计算中所研究的模型均称为膜系统,而细胞间通讯是膜系统的一个重要特征。带膜分裂的通讯膜系统是一种分布式并行计算模型,可以在多项式时间内解决计算困难问题。文中将促进剂引入带膜分裂的类细胞型通讯膜系统,提出了膜系统的一种变型——带膜分裂和促进剂的通讯膜系统,其中,一个促进剂可以同时控制多条规则,而促进剂本身不参与该条规则的进化。文中研究了带膜分裂和促进剂的通讯膜系统的计算效率,证明该类膜系统在使用同向规则长度为2,每条规则中促进剂的个数最多为1时,可以在多项式时间内求解PSPACE完全问题(QSAT问题)的统一解。     

Performance analysis of a distributed question/answering system

The problem of question/answering (Q/A) is to find answers to open-domain questions by searching large collections of documents. Unlike information retrieval systems very common today in the form of Internet search engines, Q/A systems do not retrieve documents, but instead provide short, relevant answers located in small fragments of text. This enhanced functionality comes with a price: Q/A systems are significantly slower and require more hardware resources than information retrieval systems. This paper proposes a distributed Q/A architecture that enhances the system throughput through the exploitation of interquestion parallelism and dynamic load balancing and reduces the individual question response time through the exploitation of intraquestion parallelism. Inter and intraquestion parallelism are both exploited using several scheduling points: one before the Q/A task is started and two embedded in the Q/A task. An analytical performance model is introduced. The model analyzes both the interquestion parallelism overhead generated by the migration of questions and the intraquestion parallelism overhead generated by the partitioning of the Q/A task. The analytical model indicates that both question migration and partitioning are required for a high-performance system     

Automata and processes on multisets of communicating objects

Inspired by P systems initiated by Gheorghe Pãun, we study a computation model over a multiset of communicating objects. The objects in our model are instances of finite automata. They interact with each other by firing external transitions between two objects. Our model, called a service automaton, is intended to specify, at a high level, a service provided on top of network devices abstracted as communicating objects. We formalize the concept of processes, running over a multiset of objects, of a service automaton and study the computing power of both single-process and multiprocess service automata. In particular, in the multiprocess case, regular maximal parallelism is defined for inter-process synchronization. It turns out that single-process service automata are equivalent to vector addition systems and hence can define nonregular processes. Among other results, we also show that Presburger reachability problem for single-process service automata is decidable, while it becomes undecidable in the multiprocess case. Hence, multiprocess service automata can not be effectively simulated by vector addition systems.     

一种新的组织P系统变体的研究

本文介绍了一种新的组织P系统的变体.定义的P系统改进了原始的设计,允许在通道(连接,生物上称为突触)上的规则应用中采用并行机制,以提高系统的运行效率.文中我们首先给出这种组织P系统的定义,然后描述它的运行机制,接着对它的计算能力做了一些简单的分析,并且用一个典型的例子说明了我们的P系统的运行过程的特点.     

Bond computing systems: a biologically inspired and high-level dynamics model for pervasive computing

Targeting at modeling the high-level dynamics of pervasive computing systems, we introduce bond computing systems (BCS) consisting of objects, bonds and rules. Objects are typed but addressless representations of physical or logical (computing and communicating) entities. Bonds are typed multisets of objects. In a BCS, a configuration is specified by a multiset of bonds, called a collection. Rules specify how a collection evolves to a new one. A BCS is a variation of a P system introduced by Gheorghe Paun where, roughly, there is no maximal parallelism but with typed and unbounded number of membranes, and hence, our model is also biologically inspired. In this paper, we focus on regular bond computing systems (RBCS), where bond types are regular, and study their computation power and verification problems. Among other results, we show that the computing power of RBCS lies between linearly bounded automata (LBA) and LBC (a form of bounded multicounter machines) and hence, the regular bond-type reachability problem (given an RBCS, whether there is some initial collection that can reach some collection containing a bond of a given regular type) is undecidable. We also study a restricted model (namely, B-boundedness) of RBCS where the reachability problem becomes decidable.     

Minimization strategies for maximally parallel multiset rewriting systems

Maximally parallel multiset rewriting systems (MPMRS) give a convenient way to express relations between unstructured objects. The functioning of various computational devices may be expressed in terms of MPMRS (e.g., register machines and many variants of P systems). In particular, this means that MPMRS are Turing universal; however, a direct translation leads to quite a large number of rules. Like for other classes of computationally complete devices, there is a challenge to find a universal system having the smallest number of rules. In this article we present different rule minimization strategies for MPMRS based on encodings and structural transformations. We apply these strategies to the translation of a small universal register machine (Korec (1996) [9]) and we show that there exists a universal MPMRS with 23 rules. Since MPMRS are identical to a restricted variant of P systems with antiport rules, the results we obtained improve previously known results on the number of rules for those systems.     

An approach to system design based on P/T net simulation

This work presents a technique of early simulation in the design phase of concurrent and distributed systems. A P/T net is used to model the system whose behavior is simulated by the net execution; the truly concurrent semantics of P/T nets establishes a partial order among the system events. The designer can interact with the simulator asking for measures about the system behavior that concern all executions respecting the same partial order. Some measures, such as the degree of parallelism exploited, are not easily obtainable from an interleaving semantics. Moreover, the designer can force the system behavior to reflect resource-constrained environments.     

The effectiveness of task-level parallelism for production systems

Large production systems (rule-based systems) continue to suffer from extremely slow execution which limits their utility in practical applications as well as in research settings. Most investigations in speeding up these systems have focused on match parallelism. These investigations have revealed that the total speed-up available from this source is insufficient to alleviate the problem of slow execution in large-scale production system implementations. In this paper, we focus on task-level parallelism, which is obtained by a high-level decomposition of the production system. Speed-ups obtained from task-level parallelism will multiply with the speed-ups obtained from match parallelism. The vehicle for our investigation of task-level parallelism is SPAM, a high-level vision system, implemented as a production system. SPAM is a mature research system with a typical run requiring between 50,000 and 400,000 production firings. We report very encouraging speed-ups from task-level parallelism in SPAM… -our parallel implementation shows near linear speed-ups of over 12-fold using 14 processors and points the way to substantial (50- to 100-fold) speed-ups. We present a characterization of task-level parallelism in production systems and describe our methodology for selecting and applying a particular approach to parallelize SPAM. Additionally, we report the speed-ups obtained from the use of virtual shared memory. Overall, task-level parallelism has not received much attention in the literature. Our experience illustrates that it is potentially a very important tool for speeding up large-scale production systems.