Search results for "Discrete Mathematics"
showing 10 items of 1728 documents
A loop-free two-close Gray-code algorithm for listing k-ary Dyck words
2006
AbstractP. Chase and F. Ruskey each published a Gray code for length n binary strings with m occurrences of 1, coding m-combinations of n objects, which is two-close—that is, in passing from one binary string to its successor a single 1 exchanges positions with a 0 which is either adjacent to the 1 or separated from it by a single 0. If we impose the restriction that any suffix of a string contains at least k−1 times as many 0's as 1's, we obtain k-suffixes: suffixes of k-ary Dyck words. Combinations are retrieved as special case by setting k=1 and k-ary Dyck words are retrieved as a special case by imposing the additional condition that the entire string has exactly k−1 times as many 0's a…
On parsing optimality for dictionary-based text compression—the Zip case
2013
Dictionary-based compression schemes are the most commonly used data compression schemes since they appeared in the foundational paper of Ziv and Lempel in 1977, and generally referred to as LZ77. Their work is the base of Zip, gZip, 7-Zip and many other compression software utilities. Some of these compression schemes use variants of the greedy approach to parse the text into dictionary phrases; others have left the greedy approach to improve the compression ratio. Recently, two bit-optimal parsing algorithms have been presented filling the gap between theory and best practice. We present a survey on the parsing problem for dictionary-based text compression, identifying noticeable results …
Efficient evaluation for a subset of recursive queries
1991
Abstract We consider the efficient evaluation of recursive queries in logic databases where the queries are expressed using a Datalog program (function-free Horn-clause program) that contains only regularly or linearly recursive predicates. Using well-known results on graph traversal, we develop an efficient algorithm for evaluating relations defined by a binary-chain program. We also present a transformation by which the evaluation of a subset of queries involving nonbinary relations can be reduced to the evaluation of binary-chain queries. This transformation is guided by the choice of bound arguments in the query, and the bindings are propagated through the program so that in the evaluat…
Dictionary-symbolwise flexible parsing
2012
AbstractLinear-time optimal parsing algorithms are rare in the dictionary-based branch of the data compression theory. A recent result is the Flexible Parsing algorithm of Matias and Sahinalp (1999) that works when the dictionary is prefix closed and the encoding of dictionary pointers has a constant cost. We present the Dictionary-Symbolwise Flexible Parsing algorithm that is optimal for prefix-closed dictionaries and any symbolwise compressor under some natural hypothesis. In the case of LZ78-like algorithms with variable costs and any, linear as usual, symbolwise compressor we show how to implement our parsing algorithm in linear time. In the case of LZ77-like dictionaries and any symbol…
Supervised learning of time-independent Hamiltonians for gate design
2018
We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the time-independent gate generator, thus transforming the task to an inverse eigenvalue problem. We illustrate our methodology by identifying suitable time-independent generators implementing Toffoli and Fredkin gates without the need for ancillae or effective evolutions. We show how the same conditions can be used to solve the problem numerically, via supervised learning techniques. In turn, this allows us to solve problems that are not amenable, in general, to direct ana…
Quantum versus Probabilistic One-Way Finite Automata with Counter
2001
The paper adds the one-counter one-way finite automaton [6] to the list of classical computing devices having quantum counterparts more powerful in some cases. Specifically, two languages are considered, the first is not recognizable by deterministic one-counter one-way finite automata, the second is not recognizable with bounded error by probabilistic one-counter one-way finite automata, but each recognizable with bounded error by a quantum one-counter one-way finite automaton. This result contrasts the case of one-way finite automata without counter, where it is known [5] that the quantum device is actually less powerful than its classical counterpart.
Tally languages accepted by Monte Carlo pushdown automata
1997
Rather often difficult (and sometimes even undecidable) problems become easily decidable for tally languages, i.e. for languages in a single-letter alphabet. For instance, the class of languages recognizable by 1-way nondeterministic pushdown automata equals the class of the context-free languages, but the class of the tally languages recognizable by 1-way nondeterministic pushdown automata, contains only regular languages [LP81]. We prove that languages over one-letter alphabet accepted by randomized one-way 1-tape Monte Carlo pushdown automata are regular. However Monte Carlo pushdown automata can be much more concise than deterministic 1-way finite state automata.
Upper bounds on multiparty communication complexity of shifts
1996
We consider some communication complexity problems which arise when proving lower bounds on the complexity of Boolean functions. In particular, we prove an \(O(\frac{n}{{2\sqrt {\log n} }}\log ^{1/4} n)\)upper bound on 3-party communication complexity of shifts, an O(n e ) upper bound on the multiparty communication complexity of shifts for a polylogarithmic number of parties. These bounds are all significant improvements over ones recently considered “unexpected” by Pudlak [5].
Some decisional problems on rational relations
1997
Abstract In this paper we prove that the problem of deciding whether a deterministic rational relation is star-free is recursively solvable, although the same problem for any rational relation is undecidable. We also prove that a rational relation is star-free if and only if it is aperiodic and deterministic.
Properties and constraints of cheating-immune secret sharing schemes
2006
AbstractA secret sharing scheme is a cryptographic protocol by means of which a dealer shares a secret among a set of participants in such a way that it can be subsequently reconstructed by certain qualified subsets. The setting we consider is the following: in a first phase, the dealer gives in a secure way a piece of information, called a share, to each participant. Then, participants belonging to a qualified subset send in a secure way their shares to a trusted party, referred to as a combiner, who computes the secret and sends it back to the participants.Cheating-immune secret sharing schemes are secret sharing schemes in the above setting where dishonest participants, during the recons…