Parallel Communicating Grammar Systems Research Articles

Limitations of Coverability Trees for Context-Free Parallel Communicating Grammar Systems and Why these Grammar Systems are not Linear Space

Coverability trees offer a finite characterization of all the derivations of a context-free parallel grammar system (CF-PCGS). Their finite nature implies that they necessarily omit some information about these derivations. We demonstrate that the omitted information is most if not all of the time too much, and so coverability trees are not useful as an analysis tool except for their limited use already considered in the paper that introduces them (namely, determining the decidability of certain decision problems over PCGS). We establish this result by invalidating an existing proof that synchronized CF-PCGS are less expressive than context-sensitive grammars. Indeed, we discover that this proof relies on coverability trees for CF-PCGS, but that such coverability trees do not in fact contain enough information to support the proof.

On some derivation mechanisms and the complexity of their Szilard languages

A Szilard language is a language theoretical tool used to describe the derivation process in a formal grammar or grammar system. We investigate computational resources used by (alternating) Turing machines to accept Szilard languages of Chomsky grammars, regulated grammars and grammar systems. The results are related to the circuit complexity classes NC1 and NC2. The paper is a survey of the most important complexity results in the field, but it also brings several new insights into the parallel complexity of Szilard languages of grammar systems. We focus on parallel communicating grammar systems (PCGSs) with context-free components, and we prove that the class of Szilard languages of centralized (returning or non-returning) PCGSs is included in NC1.

Memory efficient alignment between RNA sequences and stochastic grammar models of pseudoknots

Stochastic Context-Free Grammars (SCFG) has been shown to be effective in modelling RNA secondary structure for searches. Our previous work (Cai et al., 2003) in Stochastic Parallel Communicating Grammar Systems (SPCGS) has extended SCFG to model RNA pseudoknots. However, the alignment algorithm requires O(n4) memory for a sequence of length n. In this paper, we develop a memory efficient algorithm for sequence-structure alignments including pseudoknots. This new algorithm reduces the memory space requirement from O(n4) to O(n2) without increasing the computation time. Our experiments have shown that this novel approach can achieve excellent performance on searching for RNA pseudoknots.

Probabilistic Parallel Communicating Grammar Systems

Grammar systems are theoretical models of distributed computing which play a major role in modern Computer Science. In this paper, we define and study a variant of Parallel Communicating(PC) grammar systems namely, Probabilistic PC grammar systems which serves as a grammatical model for random distributed processing. We study the construct with two different models of communication protocols namely, communication by request and communication by command. We explore the generative capacity of the variant with regular, context-free and context-sensitive rules in both models of communication.

Pattern Languages Versus Parallel Communicating Grammar Systems

We compare the power of two (fairly different) recently investigated language identifying devices: patterns and parallel communicating (PC) grammar systems. The simulation of multi-patterns by context-free PC grammar systems is rather obvious, but, unexpectedly, this can be realized also by (non-centralized) PC grammar systems with right-linear components. Moreover, infinite multi-patterns forming a regular set can also be simulated by PC grammar systems with right-linear components, whereas PC grammar systems with context-free components can simulate context-free multi-patterns with context-free domains for variables.

Nonreturning PC grammar systems can be simulated by returning systems

One proves that the generative capacity of nonreturning parallel communicating (PC) grammar systems with context-free rules, centralized or not, does not overpass that of the noncentralized returning PC grammar systems. This strengthens previous results in this area and clarifies the returning-nonreturning relationship.

TWO LOWER BOUNDS ON DISTRIBUTIVE GENERATION OF LANGUAGES

The lower bounds on communication complexity measures of language generation by Parallel Communicating Grammar Systems (PCGS) are investigated. The first result shows that there exists a language that can be generated by some dag-PCGS (PCGS with communication structures realizable by directed acyclic graphs) consisting of 3 grammars, but by no PCGS with tree communication structure. The second result shows that dag-PCGS have their communication complexity of language generation either constant or linear.

Some hierarchies for the communication complexity measures of cooperating grammar systems

We investigate here the descriptional and the computational complexity of parallel communicating grammar systems (PCGS). A new descriptional complexity measure — the communication structure of the PCGS is introduced and related to the communication complexity (the number of communications). Several hierarchies resulting from these complexity measures and some relations between the measures are established. The results are obtained due to the development of two lower-bound proof techniques for PCGS. The first one is a generalization of pumping lemmas from formal language theory and the second one reduces the lower-bound problem for some PCGS to the proof of lower bounds on the number of reversals of certain sequential computing models.

On the generative capacity of parallel communicating grammar systems

The paper deals with synchronized and non-synchronized parallel communicating grammar systems (PCGS). Our results show, for instance, the high generative power of these mechanisms: one-letter non-regular and other non-semi-linear languages are generated by certain classes of PCGS's, mainly with regular components.

On the generative capacity of parallel communicating grammar systems

The paper deals with synchronized and non-synchronized parallel communicating grammar systems (PCGS). Our results show, for instance, the high generative power of these mechanisms: one-letter non-regular and other non-semi-linear languages are generated by certain classes of PCGS's, mainly with regular components.