Open AccessBook
Structural Complexity II
José L. Balcázar,Josep Díaz,Joaquim Gabarró +2 more
- 21 Dec 2011
381
TL;DR: This is the second volume of a systematic two-volume presentation of the various areas of research in the field of structural complexity, addressed to graduate students and researchers and assumes knowledge of the topics treated in the first volume but is otherwise nearly self-contained.
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Abstract: This is the second volume of a systematic two-volume presentation of the various areas of research in the field of structural complexity. The mathematical theory of computation has developed into a broad and rich discipline within which the theory of algorithmic complexity can be approached from several points of view. This volume is addressed to graduate students and researchers and assumes knowledge of the topics treated in the first volume but is otherwise nearly self-contained. Topics covered include vector machines, parallel computation, alternation, uniform circuit complexity, isomorphism, biimmunity and complexity cores, relativization and positive relativization, the low and high hierarchies, Kolmogorov complexity and probability classes. Numerous exercises and references are given.
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Citations
•Book
Complexity and Real Computation
Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale +3 more
- 30 Oct 1997
TL;DR: This chapter discusses decision problems and Complexity over a Ring and the Fundamental Theorem of Algebra: Complexity Aspects.
1.7K
Complexity and expressive power of logic programming
TL;DR: This article surveys various complexity and expressiveness results on different forms of logic programming, in particular, propositional logic programming and datalog, but it also mentions general logic programming with function symbols.
Fixed-Parameter Tractability and Completeness I: Basic Results
TL;DR: This paper establishes the main results of a completeness program which addresses the apparent fixed-parameter intractability of many parameterized problems and gives a compendium of currently known hardness results.
Computation beyond the turing limit.
TL;DR: A simply described but highly chaotic dynamical system called the analog shift map is presented here, which has computational power beyond the Turing limit (super-Turing); it computes exactly like neural networks and analog machines.
Unification: a multidisciplinary survey
TL;DR: Topics covered are resolution, higher order logic, the occur check, infinite terms, feature structures, equational theories, inheritance, parallel algorithms, generalization, lattices, and other applications of unification.
References
An Introduction To Probability Theory And Its Applications
Feller William
- 01 Jan 1950
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
10.2K
Universal classes of hash functions
TL;DR: An input independent average linear time algorithm for storage and retrieval on keys that makes a random choice of hash function from a suitable class of hash functions.
3.1K
Parity, circuits and the polynomial time hierarchy
TL;DR: A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
1.2K
On the Length of Programs for Computing Finite Binary Sequences
TL;DR: An application to the problem of defining a patternless sequence is proposed in terms of the concepts here developed to study the use of Turing machines for calculating finite binary sequences.
1.1K
Parallelism in random access machines
Steven Fortune,James C. Wyllie +1 more
- 01 May 1978
TL;DR: A model of computation based on random access machines operating in parallel and sharing a common memory is presented and can accept in polynomial time exactly the sets accepted by nondeterministic exponential time bounded Turing machines.