Results 11  20
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36
Equivalence of Models of Computation for Nearly Linear Time
, 2011
"... Theorem 1 (Main Theorem). Every nondeterministic RAM computation in time t can be simulated by a nondeterministic oblivious twotape TM in time t polylog(t). We prove this theorem in two steps. First, we show how to simulate nondeterministic RAM machines using nondeterministic multitape TMs wit ..."
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Theorem 1 (Main Theorem). Every nondeterministic RAM computation in time t can be simulated by a nondeterministic oblivious twotape TM in time t polylog(t). We prove this theorem in two steps. First, we show how to simulate nondeterministic RAM machines using nondeterministic multitape TMs
SpaceBounded Quantum Complexity
 Journal of Computer and System Sciences
, 1999
"... This paper investigates the computational power of spacebounded quantum Turing machines. The following facts are proved for spaceconstructible space bounds s satisfying s(n) = Ω(log n). 1. Any quantum Turing machine (QTM) running in space s can be simulated by an unbounded error probabilistic Tur ..."
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Cited by 27 (5 self)
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that unbounded error, space O(s) bounded quantum Turing machines and probabilistic Turing machines are equivalent in power, and furthermore that any QTM running in space s can be simulated deterministically in NC 2 (2 s) ⊆ DSPACE(s 2) ∩ DTIME ( 2 O(s)). We also consider quantum analogues of nondeterministic
Inductive TimeSpace Lower Bounds for SAT and Related Problems
 Computational Complexity
, 2005
"... Abstract. We improve upon indirect diagonalization arguments for lower bounds on explicit problems within the polynomial hierarchy. Our contributions are summarized as follows. 1. We present a technique that uniformly improves upon most known nonlinear time lower bounds for nondeterminism andalterna ..."
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Cited by 14 (4 self)
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≥ 1, there is a constant ck> 1 such that linear time with n 1/k nondeterministic bits is not contained in deterministic n ck time with subpolynomial space. This is used to prove that satisfiability of Boolean circuits with n inputs and n k size cannot be solved by deterministic multitape Turing
A Collection of Functional Libraries for Theory of Computation
 PROCEEDINGS OF THE 39TH ACMSE CONFERENCE
, 2001
"... Abstract. This paper reports the design and initial implementation of an extensive collection of libraries for automata theory and Turing machines in the functional programming languages SML and Haskell. Such an effort has two benefits: one is conceptual clarity, in the sense that computational conc ..."
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setting. In SML, we provide a simulation of finite state machines and Turing machines by taking advantage of SML's structures, functors, and exceptional handling mechanism. The simplicity of this implementation makes it valuable for classroom use. In Haskell, we provide an implementation
The P versus NP problem
 Clay Mathematical Institute; The Millennium Prize Problem
, 2000
"... The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time. To define the problem precisely it is necessary to give a formal model of a computer. The standard comp ..."
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Cited by 18 (0 self)
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. Informally the class P is the class of decision problems solvable by some algorithm within a number of steps bounded by some fixed polynomial in the length of the input. Turing was not concerned with the efficiency of his machines, rather his concern was whether they can simulate arbitrary algorithms given
Promise Problems and Access to Unambiguous Computation
, 1992
"... This paper studies the power of three types of access to unambiguous computation: nonadaptive access, faulttolerant access, and guarded access. (1) Though for NP it is known that nonadaptive access has exponentially terse adaptive simulations, we show that UP has no such relativizable simulations: ..."
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Cited by 7 (1 self)
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to recognize even sets beyond UP. Furthermore, we completely characterize, in terms of locally positive reductions, the sets that faulttolerantly reduce to UP. (3) In guarded access, Grollmann and Selman's natural notion of access to unambiguous computation, a deterministic polynomialtime Turing machine
Relationships among Time and Space Complexity Classes
, 2001
"... Multitape Turing machines are the canonical mathematical model for studying the time and space requirements of problems. Most computational problems that are efficient in practice have efficient algorithms on multitape Turing machines, and vice versa. We survey the literature on relationships amon ..."
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Cited by 1 (0 self)
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among time and space classes defined using multitape Turing machines. We discuss the result of Paul, Hopcroft and Valiant that deterministic space T is more powerful than deterministic time T and the result of Paul, Pippenger, Szemeredi and Trotter that nondeterministic linear time is more powerful than
Alternation Alternation
"... ABSTRACT. Alternation is a generalization of nondeterminism in which existential and universal quantitiers can alternate during the course of a computation, whereas in a nondeterministic computation there are only existential quantifiers. Alternating Turing machines are defined and shown to accept p ..."
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ABSTRACT. Alternation is a generalization of nondeterminism in which existential and universal quantitiers can alternate during the course of a computation, whereas in a nondeterministic computation there are only existential quantifiers. Alternating Turing machines are defined and shown to accept
Computing with Sublogarithmic Space
, 1997
"... We investigate space complexity classes defined by Turing machines that use less than logarithmic space. Because of the limited counting ability of such machines most of the standard simulation techniques do not work for sublogarithmic space classes. However, machines with such little space may stil ..."
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Cited by 3 (1 self)
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still be quite powerful. Therefore, it was not obvious how to obtain analogues for inclusion and separation results known for classes above logspace. Known facts about small spacebounded machines for deterministic, nondeterministic and alternating Turing machine models and properties
A Unified View to String Matching Algorithms
 IN PROC. THEORY AND PRACTICE OF INFORMATICS (SOFSEM'96), LNCS 1175
, 1996
"... We present a unified view to sequential algorithms for many pattern matching problems, using a finite automaton built from the pattern which uses the text as input. We show the limitations of deterministic finite automata (DFA) and the advantages of using a bitwise simulation of nondeterminis ..."
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Cited by 14 (3 self)
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We present a unified view to sequential algorithms for many pattern matching problems, using a finite automaton built from the pattern which uses the text as input. We show the limitations of deterministic finite automata (DFA) and the advantages of using a bitwise simulation of nondeterministic
Results 11  20
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36