scholarly journals A Context free language associated with interval maps

2016 ◽  
Vol Vol. 18 no. 3 ◽  
Author(s):  
M Archana ◽  
V Kannan
Keyword(s):  
Periodic Points ◽  
Interval Maps ◽  
Context Free Language ◽  
Interval Map ◽  
International Audience ◽  
Context Free ◽  
Free Language

International audience For every interval map with finitely many periodic points of periods 1 and 2, we associate a word by taking the periods of these points from left to right. It is natural to ask which words arise in this manner. In this paper we give two different characterizations of the language obtained in this way.

scholarly journals ON PERIODIC POINTS OF FREE INVERSE MONOID HOMOMORPHISMS

2013 ◽  
Vol 23 (08) ◽  
pp. 1789-1803 ◽  
Author(s):  
EMANUELE RODARO ◽  
PEDRO V. SILVA
Keyword(s):  
Fixed Point ◽  
Periodic Point ◽  
Periodic Points ◽  
Inverse Monoid ◽  
Finitely Generated ◽  
Context Sensitive ◽  
Context Free Language ◽  
Context Free ◽  
Free Language ◽  
Free Inverse Monoid

It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky's hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid can be represented by a context-sensitive language but, in general, it cannot be represented by a context-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.

scholarly journals A note on the index of a context-free language

1970 ◽  
Vol 16 (2) ◽  
pp. 201-202 ◽  
Author(s):  
Neil D. Jones
Keyword(s):  
Context Free Language ◽  
Context Free ◽  
Free Language

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.

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