Journal•ISSN: 0304-3975

# Theoretical Computer Science

About: Theoretical Computer Science is an academic journal. The journal publishes majorly in the area(s): Time complexity & Upper and lower bounds. It has an ISSN identifier of 0304-3975. Over the lifetime, 12429 publication(s) have been published receiving 345241 citation(s).

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Topics: Time complexity, Upper and lower bounds, Approximation algorithm ...read more

##### Papers

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Abstract: Alur, R. and D.L. Dill, A theory of timed automata, Theoretical Computer Science 126 (1994) 183-235. We propose timed (j&e) automata to model the behavior of real-time systems over time. Our definition provides a simple, and yet powerful, way to annotate state-transition graphs with timing constraints using finitely many real-valued clocks. A timed automaton accepts timed words-infinite sequences in which a real-valued time of occurrence is associated with each symbol. We study timed automata from the perspective of formal language theory: we consider closure properties, decision problems, and subclasses. We consider both nondeterministic and deterministic transition structures, and both Biichi and Muller acceptance conditions. We show that nondeterministic timed automata are closed under union and intersection, but not under complementation, whereas deterministic timed Muller automata are closed under all Boolean operations. The main construction of the paper is an (PSPACE) algorithm for checking the emptiness of the language of a (nondeterministic) timed automaton. We also prove that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the nondeterministic case and PSPACE-complete in the deterministic case. Finally, we discuss the application of this theory to automatic verification of real-time requirements of finite-state systems.

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6,845 citations

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TL;DR: A protocol for coin-tossing by exchange of quantum messages is presented, which is secure against traditional kinds of cheating, even by an opponent with unlimited computing power, but ironically can be subverted by use of a still subtler quantum phenomenon, the Einstein-Podolsky-Rosen paradox.

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Abstract: When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of disturbing the transmission in such a way as to be detected. Such a quantum channel can be used in conjunction with ordinary insecure classical channels to distribute random key information between two users with the assurance that it remains unknown to anyone else, even when the users share no secret information initially. We also present a protocol for coin-tossing by exchange of quantum messages, which is secure against traditional kinds of cheating, even by an opponent with unlimited computing power, but ironically can be subverted by use of a still subtler quantum phenomenon, the Einstein-Podolsky-Rosen paradox.

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4,094 citations

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TL;DR: It is shown that the permanent function of (0, 1)-matrices is a complete problem for the class of counting problems associated with nondeterministic polynomial time computations.

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Abstract: It is shown that the permanent function of (0, 1)-matrices is a complete problem for the class of counting problems associated with nondeterministic polynomial time computations. Related counting problems are also considered. The reductions used are characterized by their nontrivial use of arithmetic.

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2,776 citations

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TL;DR: A general method for proving/deciding equivalences between omega-regular languages, whose recognizers are modified forms of Buchi or Muller-McNaughton automata, derived from Milner's notion of “simulation” is obtained.

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Abstract: The paper is concerned with ways in which fair concurrency can be modelled using notations for omega-regular languages — languages containing infinite sequences, whose recognizers are modified forms of Buchi or Muller-McNaughton automata. There are characterization of these languages in terms of recursion equation sets which involve both minimal and maximal fixpoint operators. The class of ω-regular languages is closed under a fair concurrency operator. A general method for proving/deciding equivalences between such languages is obtained, derived from Milner's notion of “simulation”.

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2,196 citations

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TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.

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Abstract: It is widely believed that showing a problem to be NP -complete is tantamount to proving its computational intractability. In this paper we show that a number of NP -complete problems remain NP -complete even when their domains are substantially restricted. First we show the completeness of Simple Max Cut (Max Cut with edge weights restricted to value 1), and, as a corollary, the completeness of the Optimal Linear Arrangement problem. We then show that even if the domains of the Node Cover and Directed Hamiltonian Path problems are restricted to planar graphs, the two problems remain NP -complete, and that these and other graph problems remain NP -complete even when their domains are restricted to graphs with low node degrees. For Graph 3-Colorability, Node Cover, and Undirected Hamiltonian Circuit, we determine essentially the lowest possible upper bounds on node degree for which the problems remain NP -complete.

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2,062 citations