Search results for " complexity."
showing 10 items of 603 documents
Counting with Probabilistic and Ultrametric Finite Automata
2014
We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.
If P≠NP then some strongly noninvertible functions are invertible
2006
AbstractRabi, Rivest, and Sherman alter the standard notion of noninvertibility to a new notion they call strong noninvertibility, and show—via explicit cryptographic protocols for secret-key agreement (Rabi and Sherman attribute this protocol to Rivest and Sherman) and digital signatures (Rabi and Sherman)—that strongly noninvertible functions are very useful components in protocol design. Their definition of strong noninvertibility has a small twist (“respecting the argument given”) that is needed to ensure cryptographic usefulness. In this paper, we show that this small twist has a consequence: unless P=NP, some strongly noninvertible functions are invertible.
Two-Variable First-Order Logic with Equivalence Closure
2012
We consider the satisfiability and finite satisfiability problems for extensions of the two-variable fragment of first-order logic in which an equivalence closure operator can be applied to a fixed number of binary predicates. We show that the satisfiability problem for two-variable, first-order logic with equivalence closure applied to two binary predicates is in 2-NExpTime, and we obtain a matching lower bound by showing that the satisfiability problem for two-variable first-order logic in the presence of two equivalence relations is 2-NExpTime-hard. The logics in question lack the finite model property; however, we show that the same complexity bounds hold for the corresponding finite sa…
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
2002
This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…
Application of kolmogorov complexity to inductive inference with limited memory
1995
A b s t r a c t . We consider inductive inference with limited memory[l]. We show that there exists a set U of total recursive functions such that U can be learned with linear long-term memory (and no short-term memory); U can be learned with logarithmic long-term memory (and some amount of short-term memory); if U is learned with sublinear long-term memory, then the short-term memory exceeds arbitrary recursive function. Thus an open problem posed by Freivalds, Kinber and Smith[l] is solved. To prove our result, we use Kolmogorov complexity.
Nondeterministic Unitary OBDDs
2017
We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically “cheap” functions that are “expensive” for NUOBDDs and vice versa by improving the previous gap. We also present a function for which neither classical nor unitary nondeterminism does help. Moreover, based on our results, we present a width hierarchy for NUOBDDs. Lastly, we provide the bounds on the widths of NUOBDDs for the basic Boolean operations negation, union, and intersection.
Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs
2014
In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …
The computational complexity of the criticality problems in a network with interval activity times
2002
Abstract The paper analyzes the criticality in a network with interval activities duration times. A natural generalization of the criticality notion (for a path, an activity and an event) for the case of network with interval activity duration times is given. The computation complexity of five problems linked to the introduced criticality notion is presented.
Periodicity and repetitions in parameterized strings
2008
AbstractOne of the most beautiful and useful notions in the Mathematical Theory of Strings is that of a Period, i.e., an initial piece of a given string that can generate that string by repeating itself at regular intervals. Periods have an elegant mathematical structure and a wealth of applications [F. Mignosi and A. Restivo, Periodicity, Algebraic Combinatorics on Words, in: M. Lothaire (Ed.), Cambridge University Press, Cambridge, pp. 237–274, 2002]. At the hearth of their theory, there are two Periodicity Lemmas: one due to Lyndon and Schutzenberger [The equation aM=bNcP in a free group, Michigan Math. J. 9 (1962) 289–298], referred to as the Weak Version, and the other due to Fine and …
Quantum Finite Automata and Logics
2006
The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.