Results 1  10
of
32
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
Abstract

Cited by 1278 (4 self)
 Add to MetaCart
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.
A taxonomy for multiagent robotics
 AUTONOMOUS ROBOTS
, 1996
"... A key difficulty in the design of multiagent robotic systems is the size and complexity of the space of possible designs. In order to make principled design decisions, an understanding of the many possible system configurations is essential. To this end, we present a taxonomy that classifies multia ..."
Abstract

Cited by 97 (6 self)
 Add to MetaCart
(Show Context)
A key difficulty in the design of multiagent robotic systems is the size and complexity of the space of possible designs. In order to make principled design decisions, an understanding of the many possible system configurations is essential. To this end, we present a taxonomy that classifies multiagent systems according to communication, computational and other capabilities. We survey existing efforts involving multiagent systems according to their positions in the taxonomy. We also present additional results concerning multiagent systems, with the dual purposes of illustrating the usefulness of the taxonomy in simplifying discourse about robot collective properties, and also demonstrating that a collective can be demonstrably more powerful than a single unit of the collective.
The complexity of firstorder and monadic secondorder logic revisited
 ANNALS OF PURE AND APPLIED LOGIC
, 2004
"... ..."
The Computational Power and Complexity of Constraint Handling Rules
 In Second Workshop on Constraint Handling Rules, at ICLP05
, 2005
"... Constraint Handling Rules (CHR) is a highlevel rulebased programming language which is increasingly used for general purposes. We introduce the CHR machine, a model of computation based on the operational semantics of CHR. Its computational power and time complexity properties are compared to thos ..."
Abstract

Cited by 52 (21 self)
 Add to MetaCart
Constraint Handling Rules (CHR) is a highlevel rulebased programming language which is increasingly used for general purposes. We introduce the CHR machine, a model of computation based on the operational semantics of CHR. Its computational power and time complexity properties are compared to those of the wellunderstood Turing machine and Random Access Memory machine. This allows us to prove the interesting result that every algorithm can be implemented in CHR with the best known time and space complexity. We also investigate the practical relevance of this result and the constant factors involved. Finally we expand the scope of the discussion to other (declarative) programming languages.
The Convenience of Tilings
 In Complexity, Logic, and Recursion Theory
, 1997
"... Tiling problems provide for a very simple and transparent mechanism for encoding machine computations. This gives rise to rather simple master reductions showing various versions of the tiling problem complete for various complexity classes. We investigate the potential for using these tiling proble ..."
Abstract

Cited by 45 (0 self)
 Add to MetaCart
(Show Context)
Tiling problems provide for a very simple and transparent mechanism for encoding machine computations. This gives rise to rather simple master reductions showing various versions of the tiling problem complete for various complexity classes. We investigate the potential for using these tiling problems in subsequent reductions showing hardness of the combinatorial problems that really matter. We ilustrate our approach by means of three examples: a short reduction chain to the Knapsack problem followed by a Hilbert 10 reduction using similar ingredients. Finally we reprove the Deterministic Exponential Time lowerbound for satisfiablility in Propositional Dynamic Logic. The resulting reductions are relatively simple; they do however infringe on the principle of orthogonality of reductions since they abuse extra structure in the instances of the problems reduced from which results from the fact that these instances were generated by a master reduction previously. 1 Introduction This paper...
The tractable cognition thesis
 Cognitive Science: A Multidisciplinary Journal
, 2008
"... The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constra ..."
Abstract

Cited by 29 (6 self)
 Add to MetaCart
The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computationallevel theories of cognition. To utilize this constraint, a precise and workable definition of “computational tractability ” is needed. Following computer science tradition, many cognitive scientists and psychologists define computational tractability as polynomialtime computability, leading to the PCognition thesis. This article explains how and why the PCognition thesis may be overly restrictive, risking the exclusion of veridical computationallevel theories from scientific investigation. An argument is made to replace the PCognition thesis by the FPTCognition thesis as an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixedparameter tractable). Possible objections to the Tractable Cognition thesis, and its proposed formalization, are discussed, and existing misconceptions are clarified.
Tractable Competence
 Minds Mach
, 1998
"... In the study of cognitive processes, limitations on computational resources (computing time and memory space) are usually considered to be beyond the scope of a theory of competence, and to be exclusively relevant to the study of performance. Starting from considerations derived from the theory of c ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
In the study of cognitive processes, limitations on computational resources (computing time and memory space) are usually considered to be beyond the scope of a theory of competence, and to be exclusively relevant to the study of performance. Starting from considerations derived from the theory of computational complexity, in this paper I argue that there are good reasons for claiming that some aspects of resource limitations pertain to the domain of a theory of competence. Key words: Competence vs. performance, computational complexity, levels of cognitive explanation. 1.
A small fast universal Turing machine
 Theoretical Computer Science
, 2005
"... We present a small timeefficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time. ..."
Abstract

Cited by 16 (8 self)
 Add to MetaCart
(Show Context)
We present a small timeefficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time.