Finding the Growth Rate of a Regular of Context-Free Language in Polynomial Time

2008 ◽  
pp. 339-358 ◽  
Author(s):  
Paweł Gawrychowski ◽  
Dalia Krieger ◽  
Narad Rampersad ◽  
Jeffrey Shallit
Keyword(s):  
Growth Rate ◽  
Polynomial Time ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

FINDING THE GROWTH RATE OF A REGULAR OR CONTEXT-FREE LANGUAGE IN POLYNOMIAL TIME

2010 ◽  
Vol 21 (04) ◽  
pp. 597-618 ◽  
Author(s):  
PAWEŁ GAWRYCHOWSKI ◽  
DALIA KRIEGER ◽  
NARAD RAMPERSAD ◽  
JEFFREY SHALLIT
Keyword(s):  
Growth Rate ◽  
Polynomial Time ◽  
Exponential Growth ◽  
Polynomial Growth ◽  
Time Algorithm ◽  
Polynomial Time Algorithms ◽  
Context Free Language ◽  
Context Free ◽  
Free Language ◽  
Context Free Grammars

We give an O(n + t) time algorithm to determine whether an NFA with n states and t transitions accepts a language of polynomial or exponential growth. Given an NFA accepting a language of polynomial growth, we can also determine the order of polynomial growth in O(n+t) time. We also give polynomial time algorithms to solve these problems for context-free grammars.

scholarly journals On the Balancedness of Tree-to-Word Transducers

2021 ◽  
pp. 1-23
Author(s):  
Raphaela Löbel ◽  
Michael Luttenberger ◽  
Helmut Seidl
Keyword(s):  
Polynomial Time ◽  
Context Free Language ◽  
Non Linear ◽  
Tree Transducers ◽  
Context Free ◽  
Free Language ◽  
Output Alphabet

A language over an alphabet [Formula: see text] of opening ([Formula: see text]) and closing ([Formula: see text]) brackets, is balanced if it is a subset of the Dyck language [Formula: see text] over [Formula: see text], and it is well-formed if all words are prefixes of words in [Formula: see text]. We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time. With this at a hand we decide for the class 2-TW of non-linear tree transducers with output alphabet [Formula: see text] whether or not the output language is balanced.

scholarly journals The Insertion Encoding of Permutations

10.37236/1944 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Michael H. Albert ◽  
Steve Linton ◽  
Nik Ruškuc
Keyword(s):  
Polynomial Time ◽  
Generating Functions ◽  
Regular Language ◽  
Necessary Conditions ◽  
Polynomial Time Algorithms ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

We introduce the insertion encoding, an encoding of finite permutations. Classes of permutations whose insertion encodings form a regular language are characterized. Some necessary conditions are provided for a class of permutations to have insertion encodings that form a context free language. Applications of the insertion encoding to the evaluation of generating functions for classes of permutations, construction of polynomial time algorithms for enumerating such classes, and the illustration of bijective equivalence between classes are demonstrated.

scholarly journals A Quasi-polynomial-time Algorithm for Sampling Words from a Context-Free Language

1997 ◽  
Vol 134 (1) ◽  
pp. 59-74 ◽  
Author(s):  
Vivek Gore ◽  
Mark Jerrum ◽  
Sampath Kannan ◽  
Z. Sweedyk ◽  
Steve Mahaney
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

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.

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