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Introduction to the Theory of Computation
- M. Sipser
- Computer ScienceSIGA
Throughout the book, Sipser builds students' knowledge of conceptual tools used in computer science, the aesthetic sense they need to create elegant systems, and the ability to think through problems on their own.
Quantum Computation by Adiabatic Evolution
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that…
Parity, circuits, and the polynomial-time hierarchy
- M. Furst, J. Saxe, M. Sipser
- Computer Science22nd Annual Symposium on Foundations of Computer…
- 28 October 1981
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.
- M. Sipser, D. Spielman
- Computer ScienceProceedings 35th Annual Symposium on Foundations…
- 20 November 1994
We present a new class of asymptotically good, linear error-correcting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel…
A complexity theoretic approach to randomness
- M. Sipser
- Computer Science, MathematicsSTOC
- 1 December 1983
We study a time bounded variant of Kolmogorov complexity. This notion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within…
Private coins versus public coins in interactive proof systems
The probabilistic, nondeterministic, polynomial time Turing machine is defined and shown to be equivalent in power to the interactive proof system and to BPP much as BPP is the Probabilistic analog to P.
Nondeterminism and the size of two way finite automata
This work considers two questions on regular languages resembling these open problems of P, NP, and LOGSPACE, and 2-way non-deterministic and2-way deterministic finite automata.
GO Is Polynomial-Space Hard
It is proved that GO is Pspace hard by reducing a Pspace-complete set, TQBF, to a game called generalized geography, then to a planar version of that game, and finally to GO.