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In this paper Parikh slender context-free languages are characterized. The characterization has diverse applications. ... In a recent paper we deÿned and studied Parikh slender languages and showed that they can be used in simplifying ambiguity proofs of context-free languages. ... Parikh slender context-free languages Before the characterization of Parikh slender context-free languages we need one lemma. Lemma 8. ...doi:10.1016/s0304-3975(00)00393-5 fatcat:rptfvqxqlbcofetape6aar5hyq
., On a conjecture about slender context-free languages, Theoretical Computer Science 132 (1994) 4277434. ... We prove that every slender context-free language is a union of paired loops, thus confirming a conjecture of Paun and Salomaa to appear. ... all slender context-free languages. ...doi:10.1016/0304-3975(94)00042-5 fatcat:lutxwfiqwffdbf7shiyggszcga
Lecture Notes in Computer Science
A linear-slender context-free language is a context-free language whose number of words of length n is linear in n. ... Thanks to this characterization, we show that every linear-slender context-free language is recognizable by a real time one-way cellular automaton. ... A context-free language is poly-slender if and only if it is bounded. ...doi:10.1007/978-3-662-47221-7_19 fatcat:jnzhmozvwrg7xj5s5rto4ecuja
context-free languages. ... A similar characterization is obtained for Parikh slender context-free languages. ½ ... This improvment is based on the same characterization of poly-slender context-free languages, by  via Theorem 2.1. ...doi:10.1016/s1571-0661(05)82579-4 fatcat:aqng5oczxffvreq64w3al6hwq4
Thus, we present a length characterization for bounded context-free languages. We then study slender context-free languages, i.e., those containing at most a constant number of words of each length. ... We first show that the context-free languages for which the number of words of every length is bounded by a fixed polynomial are exactly the bounded context-free languages in the sense of Ginsburg (1966 ... Hence, L(&) is a slender linear language. 0 Every slender context-free language consists of two parts: one, the regular part, and the other, the (more interesting) context-free part. ...doi:10.1016/s0304-3975(96)00308-8 fatcat:bcsghpe6vrflfd262icx6kzije
As an application we get a new method for ambiguity proofs of context-free languages and a new proof of an earlier result of Autebert, Flajolet, and Gabarro concerning prefixes of infinite words. ] ... We define and study Parikh slender languages and power series. A language is Parikh slender if the number of words in the language with the same Parikh vector is bounded from above. ... Suppose on the contrary that L 7* is an unambiguous context-free language such that L c & R is Parikh slender, where R 7* is a regular language. (If L & R is Parikh slender the argument is similar.) ...doi:10.1006/jcss.1996.0014 fatcat:4q5xjwiecrdobnuwbsp26xll3q
Results concerning Pa&h slender languages can be applied in ambiguity proofs of context-free languages. ... In this paper an algorithm is presented for deciding whether or not a given context-free language is Parikh ... The decision method We proceed to decide whether or not a given context-free language is Par&h slender. Suppose L&C* is a context-free language. ...doi:10.1016/s0166-218x(96)00023-6 fatcat:vd6t5jsdovh35kjvvxqsqire4e
We present the basic properties of differentiation functions, especially we relate them to structure function of contextfree languages and narrow grammars to slender languages. ... We introduce the notion of a differentiation function of a context-free grammar which gives the number of terminal words that can be derived in a certain number of steps. ... (i) If L is a slender context-free matrix language, then the language σ(L) is regular. (ii) If G is a narrow context-free grammar, then the language δ(G) is regular. Proof. ...doi:10.1051/ita:2004013 fatcat:lmb5bpsctzbffn36gmwy65doqu
Context-free Parikh slender lan- guages can be characterized as finite unions of simple Dyck loop languages. ... ., context-free grammars where the applicability of rules is restricted. This allows non-context-free languages to be generated while pre- serving many positive closure and decidability properties. ...
Summary: “We survey the main results concerning slender lan- guages. We characterize slender regular and context-free languages and show that slenderness is decidable for context-free languages. ... context-free languages. ...
We give a precise characterization of the kpoly-slender context-free languages. The well-known characterization of the k-poly-slender regular languages is an immediate consequence of ours. ... For a non-negative integer k, we say that a language L is k-poly-slender if the number of words of length n in L is of order O(n k ). ... For any poly-slender context-free language L, there exists a k 0 such that # L (n) = (n k ). ...doi:10.1051/ita:2000100 fatcat:u5cp7v5dancjvn6hw2rsdhf6wa
In particular, it is shown that the slenderness decision problem is decidable for Siromoney matrix grammars with context-free rules. ... Moreover, some closure and decidability questions for slender Siromoney matrix languages are discussed. ... Moreover, a slender context-free language can effectively be written as a finite union of properly 1-slender context-free languages. ...doi:10.1016/j.ic.2008.03.024 fatcat:2j5gwmvwejgkll4yslnlgcfdba
We show a hierarchy of slender languages which is properly contained in the family of context-sensitive languages and which starts with the family of slender context-free languages, or slender regular ... Recently, it was proved that every slender regular language can be described by a finite union of terms of the form wv'w and every slender context-free language can be described by a finite union of terms ...
The present paper gives characterization results in the case of regular and context-free languages, as well as investigates decision problems. ... The paper investigates languages containing at most one word of every length, or a number of words bounded by a constant independent of the length. ... (The first one leads to context-free, the second to regular languages.) Case 1: a/b = c/d. ...doi:10.1016/0166-218x(94)00014-5 fatcat:ptxvqnkktfawtateflcslo42c4
Then one investigates context-free Parikh slender languages, making use of results about algebraic series. The main result is the following: Suppose L C V* is a context-free language. ... Summary: “There exists a regular (context-free) chain code picture language which is not described by any picture-unambiguous reg- ular (context-free) language. ...
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