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Linear indexed languages

J. Duske, R. Parchmann
1984 Theoretical Computer Science  
Furthermore t Parikh theorem for linear indexed languages is stated which implies that there are indexed languages which are not linear. O?G4.3975/84/$3.00 0 1984, Elsevier Science Publishers B.V.  ...  In this paper one characterization of linear indexed languages based on controlling linear context-free grammars with context-free languages and one based on homc.morphic images of context-free languages  ...  linear indexed languages.  ... 
doi:10.1016/0304-3975(84)90023-9 fatcat:yimpw62qjrgfpjke6qwiar3j5u

On Even Linear Indexed Languages with a Reduction to the Learning of Context-Free Languages [article]

Benjamin Caulfield
2014 arXiv   pre-print
This paper presents a restricted form of linear indexed grammars, called even linear indexed grammars, which yield the even linear indexed languages.  ...  These languages properly contain the context-free languages and are contained in the set of linear indexed languages.  ...  linear indexed language.  ... 
arXiv:1312.0175v2 fatcat:5gf3smyis5elxmwzf7ncrcng44

Logic and Rational Languages of Words Indexed by Linear Orderings

Nicolas Bedon, Alexis Bès, Olivier Carton, Chloé Rispal
2009 Theory of Computing Systems  
We prove that every rational language of words indexed by linear orderings is definable in monadic second-order logic.  ...  As a corollary we prove that the inclusion problem for rational languages of words indexed by countable linear orderings is decidable.  ...  Automata which recognize languages of words indexed by linear orderings were introduced in [4] .  ... 
doi:10.1007/s00224-009-9222-6 fatcat:ql4zjihwwfb4hc4fbppyqflqmu

A Kleene Theorem for Languages of Words Indexed by Linear Orderings [chapter]

Alexis Bès, Olivier Carton
2005 Lecture Notes in Computer Science  
A Kleene-like theorem was proved for words indexed by countable scattered linear orderings. In this paper we extend this result to languages of words indexed by all linear orderings.  ...  For instance, the empty word ε is indexed by the empty linear ordering J = ∅. Usual finite words are the words indexed by finite orderings J = {1, 2, . . . , n}, n ≥ 0.  ...  Let us finally mention the paper [20] which introduces star-free expressions for words indexed by R, and shows that starfree languages of words indexed by R coincide with languages definable in some  ... 
doi:10.1007/11505877_14 fatcat:lpwwn7tidzg3zjrlmo7vkgnjoy

A KLEENE THEOREM FOR LANGUAGES OF WORDS INDEXED BY LINEAR ORDERINGS

ALEXIS BÈS, OLIVIER CARTON
2006 International Journal of Foundations of Computer Science  
A Kleene-like theorem was proved for words indexed by countable scattered linear orderings. In this paper we extend this result to languages of words indexed by all linear orderings.  ...  For instance, the empty word ε is indexed by the empty linear ordering J = ∅. Usual finite words are the words indexed by finite orderings J = {1, 2, . . . , n}, n ≥ 0.  ...  Let us finally mention the paper [20] which introduces star-free expressions for words indexed by R, and shows that starfree languages of words indexed by R coincide with languages definable in some  ... 
doi:10.1142/s0129054106003978 fatcat:ofhndwozpzgbvlwujpxkbu6v6e

Really Natural Linear Indexed Type Checking

Arthur Azevedo de Amorim, Marco Gaboardi, Emilio Jesús Gallego Arias, Justin Hsu
2014 Proceedings of the 26nd 2014 International Symposium on Implementation and Application of Functional Languages - IFL '14  
Recent works have shown the power of linear indexed type systems for enforcing complex program properties.  ...  These systems combine linear types with a language of type-level indices, allowing more fine-grained analyses.  ...  The idea of making a limited enrichment of the index language in order to simplify type-checking may be applicable to other linear indexed type systems.  ... 
doi:10.1145/2746325.2746335 dblp:conf/ifl/AmorimGAH14 fatcat:pfntzpkrwraxtpbyyjy54otaum

Informed Source Separation of Linear Instantaneous Under-Determined Audio Mixtures by Source Index Embedding

Mathieu Parvaix, Laurent Girin
2011 IEEE Transactions on Audio, Speech, and Language Processing  
Index Terms-under-determined source separation, watermarking, audio processing, remixing.  ...  In this paper, we address the issue of underdetermined source separation of I non-stationary audio sources from a J -channel linear instantaneous mixture (J < I).  ...  If at any time index n the mixture signal can be expressed as x[n] = A · s[n] (1) where the J × I mixing matrix A is composed of constant gains, the mixture is linear instantaneous and stationary (LIS  ... 
doi:10.1109/tasl.2010.2097250 fatcat:gjoizgmkwrbj7pdjxmtsamoo5y

Logic and Rational Languages of Words Indexed by Linear Orderings [chapter]

Nicolas Bedon, Alexis Bès, Olivier Carton, Chloé Rispal
Computer Science – Theory and Applications  
A cut of a linear ordering J is a pair (K, L) of intervals such that  ...  c) ω ω 2 = ω · ω (a −ω b ω ) ω ζ · ω a ω ω ω ω r → a if r = n/2 m r → b if r ∈ Q \ {n/2 m | m ≥ 0} η x → a if x ∈ Q x → b if x ∈ R \ Q λ Operations on orderings and words Mirror image: −J backwards linear  ... 
doi:10.1007/978-3-540-79709-8_11 dblp:conf/csr/BedonBCR08 fatcat:wxowh6u2hvaibng6qrwo2sn35i

Self-embedding indexed grammars

R. Parchmann, J. Duske
1986 Theoretical Computer Science  
The notion 'self-embedding' is defined for (right-linear, linear) indexed grammars and languages, and it is shown that non self-embedding (fight-linear, linear) indexed languages are exactly the (right-linear  ...  , linear) context-free languages.  ...  A (right-linear, linear) indexed language is non self-embedding iff it is a (right-linear, linear) context-free language.  ... 
doi:10.1016/0304-3975(86)90147-7 fatcat:lupdtlbjtnhspmj74yhoohaevi

Indexed counter languages

J. Duske, M. Middendorf, R. Parchmann
1992 RAIRO - Theoretical Informatics and Applications  
A language L is called an (linear, rightlinear) index language iff L~L(G) for an (linear, rightlinear) indexed grammar G.  ...  On the other hand, consider the ic-language L={a2 n \n^\} of example 2AA. This language is not a linear indexed language since Parikh mappings of linear indexed languages are semilinear [2] .  ...  This theorem can be interpreted in the way that each type-O language can be obtained by counting on leftmost dérivations of context free grammars.  ... 
doi:10.1051/ita/1992260100931 fatcat:xuu2l2jjafgqjdeuly2akyx4fu

On Finite-Index Indexed Grammars and Their Restrictions [article]

Flavio D'Alessandro, Oscar H. Ibarra, Ian McQuillan
2016 arXiv   pre-print
The family, L(INDLIN), of languages generated by linear indexed grammars has been studied in the literature. It is known that the Parikh image of every language in L(INDLIN) is semi-linear.  ...  However, there are bounded semi linear languages that are not in L(INDLIN).  ...  A language L is said to be linear indexed if there exists a linear indexed grammar G such that L = L(G). Definition 4.  ... 
arXiv:1610.06366v3 fatcat:v4ea2oecnvhepjogjs2pm6ejsu

Page 1704 of Mathematical Reviews Vol. , Issue 86d [page]

1986 Mathematical Reviews  
Furthermore, a Parikh theorem for linear indexed languages is stated which implies that there are indexed languages which are not linear.” Ehrenfeucht, A.  ...  It is shown that the intersection of such balanced context-free resp. linear] lan- guages with the semi-Dyck language over this alphabet always yields an indexed [resp. linear indexed] language.  ... 

Rational index of bounded-oscillation languages [article]

Ekaterina Shemetova, Alexander Okhotin, Semyon Grigorev
2020 arXiv   pre-print
We investigate the rational index of bounded-oscillation languages and show that it is of polynomial order.  ...  The rational index of a context-free language L is a function f(n), such that for each regular language R recognized by an automaton with n states, the intersection of L and R is either empty or contains  ...  The family of linear languages (linear Datalog programs, respectively) is the well-known subclass of context-free languages that has polynomial rational index [5, 31] .  ... 
arXiv:2012.03567v1 fatcat:6og66bybfjgadec44uulheeowu

Cumulative subject index volumes 44–47

1980 Information and Control  
pushdown, and deterministic indexed languages, 45, 48 nondeterministic and stochastic, state transition policies for, 46, 135 semigroup, group quotient and homogeneous, 47, 59 Bin packing, stochastic  ...  Bound for binary codes outside Plotkin range, 47, 85 Griessner, codes meeting: uniqueness respecting nonexistence of, 44, 16 upper, for difference between two entropies, 45, 34 Bounded deterministic languages  ...  restoration, robustized vector recursive stabilizer algorithm for, 44, 320 indexed pushdown automata and, 45, 48 Indexed languages deterministic closure properties, 46, 200 Inductive inference  ... 
doi:10.1016/s0019-9958(80)90592-6 fatcat:zwdwzq5kifakzlpgfkl5hog2ra

Deleting Powers in Words [article]

John Machacek
2016 arXiv   pre-print
However, for deleting squares over any alphabet we find that this language can be generated by a linear index grammar which is a mildly context sensitive grammar formalism.  ...  In the general case we show that this language is generated by an indexed grammar.  ...  Similarly, a language is call a linear indexed language if it can be generated by a linear indexed grammar.  ... 
arXiv:1608.08689v1 fatcat:6rucbbcv7ndqfapovbfsmnugwu
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