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On Parikh Slender Languages and Power Series

Juha Honkala
1996 Journal of computer and system sciences (Print)  
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.  ...  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. ]  ...  Below we consider also the natural generalization of Parikh slenderness to formal power series.  ... 
doi:10.1006/jcss.1996.0014 fatcat:4q5xjwiecrdobnuwbsp26xll3q

L morphisms: Bounded delay and regularity of ambiguity [chapter]

Juha Honkala, Arto Salomaa
1991 Lecture Notes in Computer Science  
Juha Honkala: On Parikh slender languages and power series, Journal of Computer and System Sciences 52 (1996) 185-190. 18.  ...  Juha Honkala: On N-algebraic Parikh slender power series, Journal of Universal Computer Science 3 (1997) 1114-1120. 26.  ... 
doi:10.1007/3-540-54233-7_164 fatcat:7mgxxwzh2vbw3kmkaxb4bldi64

Page 2566 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
This paper gives an algorithm to test whether or not a given context-free language is Parikh slender.  ...  A language L C &* is Parikh slender if for some fixed positive integer k, the set of all w € L that have any given Parikh vector (i),-:-,i,) EN" is at most k.  ... 

Page 9260 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
For basic results concerning Parikh slender languages see Honkala [op. cit.], where it is also shown that Parikh slender languages (and power series) can be used in ambiguity proofs of context-free languages  ...  Lisovik (UKR-KIEV-A; Kiev) 2002m:68061 68Q45 68Q25 Honkala, Juha (FIN-TURK; Turku) On Parikh slender context-free languages. (English summary) Theoret. Comput. Sci. 255 (2001), no. 1-2, 667-677.  ... 

Page 1198 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Katsushi Inoue (J-YAMASE-SE; Ube) 97b:68108 68Q45 68Q70 Honkala, Juha (FIN-TURK; Turku) On Parikh slender languages and power series. (English summary) J. Comput.  ...  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.  ... 

Page 5697 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
Summary: “In a recent paper we introduced Parikh slender lan- guages and series as a generalization of slender languages defined and studied by Andrasiu, Dassow, Paun and Salomaa.  ...  5697 99h:68104 68Q45 Honkala, Juha (FIN-TURK; Turku) On N-algebraic Parikh slender power series. (English summary) J.UCS 3 (1997), no. 10, 1114-1120 (electronic).  ... 

On Parikh slender context-free languages

Juha Honkala
2001 Theoretical Computer Science  
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.  ...  In this paper Parikh slender context-free languages are characterized. The characterization has diverse applications.  ...  For basic results concerning Parikh slender languages see Honkala [8] , where it is also shown that Parikh slender languages (and power series) can be used in ambiguity proofs of context-free languages  ... 
doi:10.1016/s0304-3975(00)00393-5 fatcat:rptfvqxqlbcofetape6aar5hyq

Page 2063 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
A cyclic language L on A is a subset of A* that is closed under all powers, all roots and conjugation.  ...  The notions of Parikh thin and Parikh slender languages are defined similarly by counting the words with the same Parikh vectors instead of the words of the same length.  ... 

The Parikh counting functions of sparse context-free languages are quasi-polynomials

Flavio D'Alessandro, Benedetto Intrigila, Stefano Varricchio
2009 Theoretical Computer Science  
Let L be a sparse context-free language over an alphabet of t letters and let f L : N t → N be its Parikh counting function. We prove the following two results: 1.  ...  There exists a partition of N t into a finite family of rational subsets such that the function f L is a polynomial on each set of the partition.  ...  Acknowledgement The authors would like to thank Corrado De Concini for very useful comments and discussions concerning the results presented in the first part of the paper.  ... 
doi:10.1016/j.tcs.2009.09.006 fatcat:svzkva7myff6hpfmq7zsbav7oy

The Parikh functions of sparse context-free languages are quasi-polynomials [article]

Flavio D'Alessandro, Benedetto Intrigila, Stefano Varricchio
2008 arXiv   pre-print
We prove that the Parikh map of a bounded context-free language is a box spline. Moreover we prove that in this case, such a function is rational.  ...  The authors would like to thank Corrado De Concini for very useful comments and discussions concerning the results presented in the first part of the paper.  ...  In particular, one can decide whether a context-free language is Parikh thin or Parikh slender [13] .  ... 
arXiv:0807.0718v1 fatcat:m66dm5vc2vhfvjqbk3zyvs46wm

On lengths of words in context-free languages

Lucian Ilie
2000 Theoretical Computer Science  
These upper bounds depend on the given language only. Using this result, we give two new and simple proofs for the decidability of the slenderness problem for context-free languages.  ...  We consider slender languages, that is, languages for which the number of words of the same length is bounded from above by a constant.  ...  Also, I thank an anonymous referee for suggesting the result of Ginsburg and Spanier on bounded languages.  ... 
doi:10.1016/s0304-3975(98)00266-7 fatcat:6rper3rhjneglevbwz56qtrp3y

On D0L power series

Juha Honkala
2000 Theoretical Computer Science  
cients in D0L power series and establish various decidability results.  ...  We study D0L power series.  ...  Now the characterization of slender regular languages (see [24] ) implies that there exist words u; v; w ∈ X * such that the language L ∩ u v * w is inÿnite and v is primitive.  ... 
doi:10.1016/s0304-3975(98)00338-7 fatcat:wn7uaiegdfgb5fmyuasg4eqxgm

L Systems [chapter]

Lila Kari, Grzegorz Rozenberg, Arto Salomaa
1997 Handbook of Formal Languages  
From the point of view of power series, [SS] , [KS] , this means several noncommuting variables.  ...  The converse does not hold true: the language fb i ab i j i 0g[ fb 2i+1 j i 0g is a slender 0L language not generated by any derivation-slender 0L system.  ... 
doi:10.1007/978-3-642-59136-5_5 fatcat:5evlmahr75dadkiqepxf7rqkf4

Page 1640 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
(English summary) 99¢:68152 — Decision problems concerning a power series generalization of DTOL systems. (English summary) 99i:68075 — On N-algebraic Parikh slender power series.  ...  (English summary) 99h:68104 — Decision problems concerning thinness and slenderness of formal languages. (English summary) 99¢:68153 — On slender languages.  ... 

Page 2034 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
., 2003d:68167 Kudlek, Manfred see Démési, Pal, 2003k:68057 Kuich, Werner Automata on power series and tree automata on tree series.  ...  et al., 2003):68089 Ibarra, Oscar H. sce Dang, Zhe et al., 2003k:68073 and (2003e:68005 ) Iie, Lucian On generalized slenderness of context-free languages.  ... 
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