Recursively enumerable language

About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.

Splicing Systems over Permutation Groups of Length Two

Abstract: The first theoretical model of DNA computing, called a splicing system, for the study of the generative power of deoxyribonucleic acid (DNA) in the presence of restriction enzymes and ligases was introduced by Head in 1987. Splicing systems model the recombinant behavior of double-stranded DNA (dsDNA) and the enzymes which perform operation of cutting and pasting on dsDNA. Splicing systems with finite sets of axioms and rules generate only regular languages when no additional control is assumed. With several restrictions to splicing rules, the generative power increase up to recursively enumerable languages. Algebraic structures can also be used in order to control the splicing systems. In the literature, splicing systems with additive and multiplicative valences have been investigated, and it has been shown that the family of languages generated by valence splicing systems is strictly included in the family of context-sensitive languages. This motivates the study of splicing systems over permutation groups. In this paper, we define splicing systems over permutation groups and investigate the generative power of the languages produced.

Instant Computing - A New Computation Paradigm

Abstract: Voltage peaks on a conventional computer's power lines allow for the well-known dangerous DPA attacks. We show that measurement of a quantum computer's transient state during a computational step reveals information about a complete computation of arbitrary length, which can be extracted by repeated probing, if the computer is suitably programmed. Instant computing, as we name this mode of operation, recognizes for any total or partial recursive function arguments lying in the domain of definition and yields their function value with arbitrary small error probability in probabilistic linear time. This implies recognition of (not necessarily recursively enumerable) complements of recursively enumerable sets and the solution of the halting problem. Future quantum computers are shown to be likely to allow for instant computing, and some consequences are pointed out.

Communicating processes, scheduling and the complexity of nontermination

Abstract: In this paper we study the computational complexity of the nontermination problem for systems of communicating processes with respect to five types of scheduling schemes, namely, round-robin, random, priority, first-come-first-served, and equifair schedules. We show that the problem is undecidable (Π1-complete) with respect to round-robin, first-come-first-served, and priority scheduling; whereas it is decidable with respect to random and equifair scheduling. (Here Π1 denotes the set of languages whose complements are recursively enumerable.) For a restricted class of systems in which the communication channels between processes are of unit capacity, we show that the nontermination problem is solvable inO(k2 logn) nondeterministic space for round-robin, random, priority, and first-come-first-served scheduling, and inno(k2) nondeterministic time for equifair scheduling, wherek is the number of processes andn is the size of the maximal process. We are also able to establish a lower bound of Ω((k−59)/20*logn) nondeterministic space for all five types of scheduling schemes.