662 research outputs found
Generating all permutations by context-free grammars in Chomsky normal form
Let Ln be the finite language of all n! strings that are permutations of n different symbols (n1). We consider context-free grammars Gn in Chomsky normal form that generate Ln. In particular we study a few families {Gn}n1, satisfying L(Gn)=Ln for n1, with respect to their descriptional complexity, i.e. we determine the number of nonterminal symbols and the number of production rules of Gn as functions of n
Generating All Permutations by Context-Free Grammars in Greibach Normal Form
We consider context-free grammars in Greibach normal form and, particularly, in Greibach -form () which generates the finite language of all strings that are permutations of different symbols (). These grammars are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of as functions of . As in the case of Chomsky normal form these descriptional complexity measures grow faster than any polynomial function
An infinite hierarchy of languages defined by dP systems
Here, we continue the study of the recently introduced dP automata. They are
symport/antiport P systems consisting of a number of components, each one accepting a
string, and working together in recognizing the concatenation of these separate strings;
the overall string is distributed to the dP automaton components in a balanced way, i.e.,
in equal parts up to one symbol, like in the communication complexity area. The question
whether or not the number of components induces an infinite hierarchy of the recognized
languages was formulated as an open problem in the literature.Wesolve here affirmatively
this question (by connecting P automata with right linear simple matrix grammars), then
we also briefly discuss the relation between the balanced and the non-balanced way of
splitting the input string among components; settling this latter problem remains as a
research topic. Some other open problems are also formulated.Junta de Andalucía P08-TIC-0420
On Buffon Machines and Numbers
The well-know needle experiment of Buffon can be regarded as an analog (i.e.,
continuous) device that stochastically "computes" the number 2/pi ~ 0.63661,
which is the experiment's probability of success. Generalizing the experiment
and simplifying the computational framework, we consider probability
distributions, which can be produced perfectly, from a discrete source of
unbiased coin flips. We describe and analyse a few simple Buffon machines that
generate geometric, Poisson, and logarithmic-series distributions. We provide
human-accessible Buffon machines, which require a dozen coin flips or less, on
average, and produce experiments whose probabilities of success are expressible
in terms of numbers such as, exp(-1), log 2, sqrt(3), cos(1/4), aeta(5).
Generally, we develop a collection of constructions based on simple
probabilistic mechanisms that enable one to design Buffon experiments involving
compositions of exponentials and logarithms, polylogarithms, direct and inverse
trigonometric functions, algebraic and hypergeometric functions, as well as
functions defined by integrals, such as the Gaussian error function.Comment: Largely revised version with references and figures added. 12 pages.
In ACM-SIAM Symposium on Discrete Algorithms (SODA'2011
Permuting operations on strings and their relation to prime numbers
Some length-preserving operations on strings only permute the symbol positions in strings; such an operation gives rise to a family of similar permutations. We investigate the structure and the order of the cyclic group generated by . We call an integer -{\em prime} if consists of a single cycle of length (). Then we show some properties of these -primes, particularly, how -primes are related to -primes as well as to ordinary prime numbers. Here and range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on Archimedes spiral and on the Josephus problem
On the structure of context-sensitive grammars
Context sensitive grammar and generation of noncontext free language
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