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.

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.

THE EDIT-DISTANCE BETWEEN A REGULAR LANGUAGE AND A CONTEXT-FREE LANGUAGE

2013 ◽  
Vol 24 (07) ◽  
pp. 1067-1082 ◽  
Author(s):  
YO-SUB HAN ◽  
SANG-KI KO ◽  
KAI SALOMAA
Keyword(s):  
Regular Language ◽  
Edit Distance ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The Other ◽  
Optimal Alignment ◽  
Worst Case ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

The edit-distance between two strings is the smallest number of operations required to transform one string into the other. The distance between languages L1and L2is the smallest edit-distance between string wi∈ Li, i = 1, 2. We consider the problem of computing the edit-distance of a given regular language and a given context-free language. First, we present an algorithm that finds for the languages an optimal alignment, that is, a sequence of edit operations that transforms a string in one language to a string in the other. The length of the optimal alignment, in the worst case, is exponential in the size of the given grammar and finite automaton. Then, we investigate the problem of computing only the edit-distance of the languages without explicitly producing an optimal alignment. We design a polynomial time algorithm that calculates the edit-distance based on unary homomorphisms.

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 On the Commutative Equivalence of Algebraic Formal Series and Languages

2021 ◽  
pp. 1-27
Author(s):  
Arturo Carpi ◽  
Flavio D’Alessandro
Keyword(s):  
Exponential Growth ◽  
Regular Language ◽  
Formal Series ◽  
Regular Languages ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

The problem of the commutative equivalence of context-free and regular languages is studied. Conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated.

The word problem of ℤ n is a multiple context-free language

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Meng-Che Ho
Keyword(s):  
Word Problem ◽  
Regular Language ◽  
Formal Languages ◽  
Strong Connection ◽  
Context Free Language ◽  
Multiple Context ◽  
Context Free ◽  
Free Language

Abstract The word problem of a group {G=\langle\Sigma\rangle} can be defined as the set of formal words in {\Sigma^{*}} that represent the identity in G. When viewed as formal languages, this gives a strong connection between classes of groups and classes of formal languages. For example, Anīsīmov showed that a group is finite if and only if its word problem is a regular language, and Muller and Schupp showed that a group is virtually-free if and only if its word problem is a context-free language. Recently, Salvati showed that the word problem of {\mathbb{Z}^{2}} is a multiple context-free language, giving the first example of a natural word problem that is multiple context-free, but not context-free. We generalize Salvati’s result to show that the word problem of {\mathbb{Z}^{n}} is a multiple context-free language for any n.

HOLONOMIC GENERATING FUNCTIONS AND CONTEXT FREE LANGUAGES

1992 ◽  
Vol 03 (02) ◽  
pp. 181-191 ◽  
Author(s):  
A. BERTONI ◽  
P. MASSAZZA ◽  
N. SABADINI
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Equivalence Problem ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

In this paper we give some undecidability and decidability results about context-free languages. First, we prove that the problem of deciding whether a context-free language which admits a holonomic generating function is Turing equivalent to the finiteness question for r.e. sets. Second, we show that the Equivalence Problem is decidable for a suitable class of languages, called LCLR.

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
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