268 research outputs found
Computation with narrow CTCs
We examine some variants of computation with closed timelike curves (CTCs),
where various restrictions are imposed on the memory of the computer, and the
information carrying capacity and range of the CTC. We give full
characterizations of the classes of languages recognized by polynomial time
probabilistic and quantum computers that can send a single classical bit to
their own past. Such narrow CTCs are demonstrated to add the power of limited
nondeterminism to deterministic computers, and lead to exponential speedup in
constant-space probabilistic and quantum computation. We show that, given a
time machine with constant negative delay, one can implement CTC-based
computations without the need to know about the runtime beforehand.Comment: 16 pages. A few typo was correcte
Memoization for Unary Logic Programming: Characterizing PTIME
We give a characterization of deterministic polynomial time computation based
on an algebraic structure called the resolution semiring, whose elements can be
understood as logic programs or sets of rewriting rules over first-order terms.
More precisely, we study the restriction of this framework to terms (and logic
programs, rewriting rules) using only unary symbols. We prove it is complete
for polynomial time computation, using an encoding of pushdown automata. We
then introduce an algebraic counterpart of the memoization technique in order
to show its PTIME soundness. We finally relate our approach and complexity
results to complexity of logic programming. As an application of our
techniques, we show a PTIME-completeness result for a class of logic
programming queries which use only unary function symbols.Comment: Soumis {\`a} LICS 201
Alternating and empty alternating auxiliary stack automata
AbstractWe consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited. In this way we get new characterizations of NP, the polynomial hierarchy, PSpace, and bounded query classes like co-DP=NLăNP[1]ă and Î2P=PNP[O(logn)], in a uniform framework
Tree-size bounded alternation
AbstractThe size of an accepting computation tree of an alternating Turing machine (ATM) is introduced as a complexity measure. We present a number of applications of tree-size to the study of more traditional complexity classes. Tree-size on ATMs is shown to closely correspond to time on nondeterministic TMs and on nondeterministic auxiliary pushdown automata. One application of the later is a useful new characterization of the class of languages log-space-reducible to context-free languages. Surprising relationships with parallel-time complexity are also demonstrated. ATM computations using at most space S(n) and tree-size Z(n) (simultaneously) can be simulated in alternating space S(n) and time S(n) · log Z(n) (simultaneously). Several well-known simulations, e.g., Savitch's theorem, are special cases of this result. It also leads to improved parallel complexity bounds for many problems in terms of both time and number of âprocessors.â As one example we show that context-free language recognition in time O(log2 n) is possible on several parallel models. Further, this bound is achievable with only a polynomial number of processors, in contrast to all previously known sub-linear time CFL recognizers
Logspace self-reducibility
A definition of self-reducibility is proposed to deal with logarithmic space complexity classes. A general property derived from the definition is used to prove known results comparing uniform and nonuniform complexity classes below polynomial time, and to obtain novel ones regarding nondeterministic nonuniform classes and reducibility to context-free languages.Peer ReviewedPostprint (published version
Positive Versions of Polynomial Time
AbstractWe show that restricting a number of characterizations of the complexity classPto be positive (in natural ways) results in the same class of (monotone) problems, which we denote byposP. By a well-known result of Razborov,posPis a proper subclass of the class of monotone problems inP. We exhibit complete problems forposPvia weak logical reductions, as we do for other logically defined classes of problems. Our work is a continuation of research undertaken by Grigni and Sipser, and subsequently Stewart; indeed, we introduce the notion of a positive deterministic Turing machine and consequently solve a problem posed by Grigni and Sipser
Comparative Schematology and Pebbling with Auxiliary Pushdowns
This paper has three claims to interest. First, it combines comparative schematology with complexity theory. This combination is capable of distinguishing among Strong\u27s âlanguages of maximal power,â a distinction not possible when comparative schematology is based on computability considerations alone, and it is capable of establishing exponential disparities in running times, a capability not currently possessed by complexity theory alone. Secondly, this paper inaugurates the study of pebbling with auxiliary pushdowns, which bears to plain pebbling the same relationship as Cook\u27s study of space-bounded machines with auxiliary pushdowns bears to plain space-bounded machines. This extension of pebbling serves as the key to the problems of comparative schematology mentioned above. Finally, this paper advantageously displays the virtues of recent work by Gabber and Galil giving explicit constructions for certain graphs, for the availability of such explicit constructions is essential to the results of this paper
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