Uniform Random Generation of Strings in a Context-Free Language

1983 ◽  
Vol 12 (4) ◽  
pp. 645-655 ◽  
Author(s):  
Timothy Hickey ◽  
Jacques Cohen
Keyword(s):  
Random Generation ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

scholarly journals Multi-dimensional Boltzmann Sampling of Languages

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Olivier Bodini ◽  
Yann Ponty
Keyword(s):  
Frequency Of Occurrence ◽  
Random Generation ◽  
Tolerance Intervals ◽  
Strong Connectivity ◽  
Expected Time ◽  
Context Free Language ◽  
Different Types ◽  
International Audience ◽  
Context Free ◽  
Free Language

International audience We address the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers. We show that, under mostly $\textit{strong-connectivity}$ hypotheses, our samplers return a word of size in $[(1- \epsilon)n, (1+ \epsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega (\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate our approach on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.

WHEN CHURCH-ROSSER BECOMES CONTEXT FREE

2007 ◽  
Vol 18 (06) ◽  
pp. 1293-1302 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER
Keyword(s):  
Linear Time ◽  
Membership Problem ◽  
Closure Properties ◽  
Context Free Language ◽  
Arithmetic Hierarchy ◽  
Context Free ◽  
Free Language

We investigate the intersection of Church-Rosser languages and (strongly) context-free languages. The intersection is still a proper superset of the deterministic context-free languages as well as of their reversals, while its membership problem is solvable in linear time. For the problem whether a given Church-Rosser or context-free language belongs to the intersection we show completeness for the second level of the arithmetic hierarchy. The equivalence of Church-Rosser and context-free languages is Π1-complete. It is proved that all considered intersections are pairwise incomparable. Finally, closure properties under several operations are investigated.

Layered Region Based Flow-Sensitive Demand-Driven Alias Analysis

2014 ◽  
Vol 577 ◽  
pp. 917-920
Author(s):  
Long Pang ◽  
Xiao Hong Su ◽  
Pei Jun Ma ◽  
Ling Ling Zhao
Keyword(s):  
Program Analysis ◽  
Control Flow ◽  
Alias Analysis ◽  
Reachability Problem ◽  
Analysis Algorithm ◽  
Context Free Language ◽  
Context Free ◽  
Free Language ◽  
Demand Driven Analysis

The pointer alias is indispensable for program analysis. Comparing to point-to set, it’s more efficient to formulate the alias as the context free language (CFL) reachability problem. However, the precision is limited to flow-insensitivity. To solve this problem, we propose a flow sensitive, demand-driven analysis algorithm for answering may-alias queries. First the partial single static assignment is used to discriminate the address-taken pointers. Then the order of control flow is encoded in the level linearization code to ease comparison. Finally, the query of alias in demand driven is converted into the search of CFL reachability with feasible flows. The experiments demonstrate the effectiveness of the proposed approach.

scholarly journals Growth in Baumslag–Solitar groups I: subgroups and rationality

2011 ◽  
Vol 14 ◽  
pp. 34-71 ◽  
Author(s):  
Eric M. Freden ◽  
Teresa Knudson ◽  
Jennifer Schofield
Keyword(s):  
Turing Machine ◽  
Time Complexity ◽  
Machine Construction ◽  
Convolution Product ◽  
Growth Series ◽  
Context Sensitive ◽  
Context Free Language ◽  
Time And Space Complexity ◽  
Context Free ◽  
Free Language

AbstractThe computation of growth series for the higher Baumslag–Solitar groups is an open problem first posed by de la Harpe and Grigorchuk. We study the growth of the horocyclic subgroup as the key to the overall growth of these Baumslag–Solitar groups BS(p,q), where 1<p<q. In fact, the overall growth series can be represented as a modified convolution product with one of the factors being based on the series for the horocyclic subgroup. We exhibit two distinct algorithms that compute the growth of the horocyclic subgroup and discuss the time and space complexity of these algorithms. We show that when p divides q, the horocyclic subgroup has a geodesic combing whose words form a context-free (in fact, one-counter) language. A theorem of Chomsky–Schützenberger allows us to compute the growth series for this subgroup, which is rational. When p does not divide q, we show that no geodesic combing for the horocyclic subgroup forms a context-free language, although there is a context-sensitive geodesic combing. We exhibit a specific linearly bounded Turing machine that accepts this language (with quadratic time complexity) in the case of BS(2,3) and outline the Turing machine construction in the general case.

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