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

Finite automata with advice tapes

We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.Comment: Corrected typo

How Fast Can We Multiply Large Integers on an Actual Computer?

We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity of a task like multiplication of long integers. The Turing machine is more useful here, but fails to take into account the multiplication instruction for short integers, which is available on physical computing devices. An interesting outcome is that the proposed refined complexity measures do not rank the well known multiplication algorithms the same way as the Turing machine model.Comment: To appear in the proceedings of Latin 2014. Springer LNCS 839

A sound and complete semantics for a version of negation as failure

AbstractNegation as failure is sound both for the closed world assumption and the completed database or completion, comp(P) of a program P. In general it is not complete for either of these declarative semantics. Indeed there can be no semantics for which it is both sound and complete, for all programs and queries, because non-ground negative literals cannot be dealt with, and cause floundering. By extending the negation as failure rule we exclude floundering and we give a semantics T̄ω(P) for which the extended rule is both sound and complete. T̄ω(P) is a weak version of comp(P) based on an iterative construction. We show that the soundness and completeness results still hold if the classical consequence relation ⊢ is replaced by a weaker relation ⊢31 which is sound for both 3-valued logic and intuitionistic logic