Shankara Narayanan Krishna

P Systems with Mobile Membranes

P systems with active membranes are among the central ones in membrane computing, and they were shown to be both computationally universal (able to simulate Turing machines) and computationally efficient (able to solve hard problems in polynomial time). However, in all cases, these results were obtained by making use of several powerful features, such as membrane polarization, label changing, division of non-elementary membranes, priorities, or cooperative rules. This paper contributes to the research effort of introducing a class of P systems with active membranes having none of the features mentioned above, but still preserving the power and the efficiency. The additional feature we consider instead are the operations of endocytosis and exocytosis: moving a membrane inside a neighboring membrane, or outside the membrane where it is placed. We investigate the power and the efficiency of these systems (also using membrane division) by first proving that they can simulate (with a linear slowdown and without introducing non-determinism) rewriting P systems with 2-replication, for which the universality and the possibility of solving NP-complete problems in polynomial time are known. In this way, the universality and efficiency are also obtained for our systems. We also give a direct and simple proof for the universality result – without using division rules (the proof uses nine membranes, but we do not know whether this number can be decreased).

Universality results for P systems based on brane calculi operations

Operations with membranes are essential both in brane calculi as well as in membrane computing. In this paper, we attempt to express six basic operations of brane calculi, viz., pino, exo, phago, bud, mate, drip in terms of the membrane computing formalism. We also investigate the computing power of P systems controlled by phago/exo, pino/exo, bud/mate as well as the mate/drip operations. We give an improvement to a characterization of RE using mate/drip operations given in [L. Cardelli, Gh. Paun, An universality result based on mate/drip operations, International Journal of Foundations of Computer Science (in press)]. We also give a characterization of RE using a new operation, called selective mate. We conjecture that it is not possible to obtain Turing completeness using only one of the six operations. We also conjecture that the pairs of operations we have considered for completeness, in this paper, are complete: it is impossible to obtain Turing completeness with any other pair of operations.

Compositional Verification of Software Product Lines

This paper presents a novel approach to the design verification of Software Product Lines (SPL). The proposed approach assumes that the requirements and designs at the feature level are modeled as finite state machines with variability information. The variability information at the requirement and design levels are expressed differently and at different levels of abstraction. Also the proposed approach supports verification of SPL in which new features and variability may be added incrementally. Given the design and requirements of an SPL, the proposed design verification method ensures that every product at the design level behaviourally conforms to a product at the requirement level. The conformance procedure is compositional in the sense that the verification of an entire SPL consisting of multiple features is reduced to the verification of the individual features. The method has been implemented and demonstrated in a prototype tool SPLEnD (SPL Engine for Design Verification) on a couple of fairly large case studies.

Timed Automata with Integer Resets: Language Inclusion and Expressiveness

In this paper, we consider a syntactic subset of timed automata called integer reset timed automata (IRTA) where resetsare restricted to occur at integral time points. We argue with examples that the notion of global sparse time base used in time triggered architecture and distributed web services can naturally be modelled/specified as IRTA. As our main result, we show that the language inclusion problem

Results on catalytic and evolution-communication P systems

L(\mathcal A) \subseteq L(\mathcal{B})

The power of mobility: four membranes suffice

for a timed automaton

Tracing SPLs precisely and efficiently

\mathcal A

On the Computational Power of Enhanced Mobile Membranes

and an IRTA

Matrix insertion-deletion systems for bio-molecular structures

\mathcal{B}

Modal strength reduction in quantified discrete duration calculus

is decidable with EXPSPACE complexity. The expressive power and the closure properties of IRTA are also summarized. In particular, the IRTA are (highly succinct but) expressively equivalent to 1-clock deterministic IRTA and they are closed under boolean operations.