6,994 research outputs found
On the Commutative Equivalence of Context-Free Languages
The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated
Partially-commutative context-free languages
The paper is about a class of languages that extends context-free languages
(CFL) and is stable under shuffle. Specifically, we investigate the class of
partially-commutative context-free languages (PCCFL), where non-terminal
symbols are commutative according to a binary independence relation, very much
like in trace theory. The class has been recently proposed as a robust class
subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We
identify a natural corresponding automaton model: stateless multi-pushdown
automata. We show stability of the class under natural operations, including
homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to
two other relevant classes: CFL extended with shuffle and trace-closures of
CFL. Among technical contributions of the paper are pumping lemmas, as an
elegant completion of known pumping properties of regular languages, CFL and
commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Tightening the Complexity of Equivalence Problems for Commutative Grammars
We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page
Complexity of Problems of Commutative Grammars
We consider commutative regular and context-free grammars, or, in other
words, Parikh images of regular and context-free languages. By using linear
algebra and a branching analog of the classic Euler theorem, we show that,
under an assumption that the terminal alphabet is fixed, the membership problem
for regular grammars (given v in binary and a regular commutative grammar G,
does G generate v?) is P, and that the equivalence problem for context free
grammars (do G_1 and G_2 generate the same language?) is in
Tree Languages Defined in First-Order Logic with One Quantifier Alternation
We study tree languages that can be defined in \Delta_2 . These are tree
languages definable by a first-order formula whose quantifier prefix is forall
exists, and simultaneously by a first-order formula whose quantifier prefix is
. For the quantifier free part we consider two signatures, either the
descendant relation alone or together with the lexicographical order relation
on nodes. We provide an effective characterization of tree and forest languages
definable in \Delta_2 . This characterization is in terms of algebraic
equations. Over words, the class of word languages definable in \Delta_2 forms
a robust class, which was given an effective algebraic characterization by Pin
and Weil
Varieties of Cost Functions.
Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalising two results on regular languages to cost functions: Eilenberg's varieties theorem and profinite equational characterisations of lattices of regular languages. This opens interesting new perspectives, but the specificities of cost functions introduce difficulties that prevent these generalisations to be straightforward. In contrast, although syntactic algebras can be defined for formal power series over a commutative ring, no such notion is known for series over semirings and in particular over the tropical semiring
Generalized Results on Monoids as Memory
We show that some results from the theory of group automata and monoid
automata still hold for more general classes of monoids and models. Extending
previous work for finite automata over commutative groups, we demonstrate a
context-free language that can not be recognized by any rational monoid
automaton over a finitely generated permutable monoid. We show that the class
of languages recognized by rational monoid automata over finitely generated
completely simple or completely 0-simple permutable monoids is a semi-linear
full trio. Furthermore, we investigate valence pushdown automata, and prove
that they are only as powerful as (finite) valence automata. We observe that
certain results proven for monoid automata can be easily lifted to the case of
context-free valence grammars.Comment: In Proceedings AFL 2017, arXiv:1708.0622
On the rational subset problem for groups
We use language theory to study the rational subset problem for groups and
monoids. We show that the decidability of this problem is preserved under graph
of groups constructions with finite edge groups. In particular, it passes
through free products amalgamated over finite subgroups and HNN extensions with
finite associated subgroups. We provide a simple proof of a result of
Grunschlag showing that the decidability of this problem is a virtual property.
We prove further that the problem is decidable for a direct product of a group
G with a monoid M if and only if membership is uniformly decidable for
G-automata subsets of M. It follows that a direct product of a free group with
any abelian group or commutative monoid has decidable rational subset
membership.Comment: 19 page
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