1,545 research outputs found
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
Cone types and geodesic languages for lamplighter groups and Thompson's group F
We study languages of geodesics in lamplighter groups and Thompson's group F.
We show that the lamplighter groups have infinitely many cone types, have
no regular geodesic languages, and have 1-counter, context-free and counter
geodesic languages with respect to certain generating sets. We show that the
full language of geodesics with respect to one generating set for the
lamplighter group is not counter but is context-free, while with respect to
another generating set the full language of geodesics is counter and
context-free. In Thompson's group F with respect to the standard finite
generating set, we show there are infinitely many cone types and no regular
language of geodesics with respect to the standard finite generating set. We
show that the existence of families of "seesaw" elements with respect to a
given generating set in a finitely generated infinite group precludes a regular
language of geodesics and guarantees infinitely many cone types with respect to
that generating set.Comment: 30 pages, 13 figure
Decidable Classes of Tree Automata Mixing Local and Global Constraints Modulo Flat Theories
We define a class of ranked tree automata TABG generalizing both the tree
automata with local tests between brothers of Bogaert and Tison (1992) and with
global equality and disequality constraints (TAGED) of Filiot et al. (2007).
TABG can test for equality and disequality modulo a given flat equational
theory between brother subterms and between subterms whose positions are
defined by the states reached during a computation. In particular, TABG can
check that all the subterms reaching a given state are distinct. This
constraint is related to monadic key constraints for XML documents, meaning
that every two distinct positions of a given type have different values. We
prove decidability of the emptiness problem for TABG. This solves, in
particular, the open question of the decidability of emptiness for TAGED. We
further extend our result by allowing global arithmetic constraints for
counting the number of occurrences of some state or the number of different
equivalence classes of subterms (modulo a given flat equational theory)
reaching some state during a computation. We also adapt the model to unranked
ordered terms. As a consequence of our results for TABG, we prove the
decidability of a fragment of the monadic second order logic on trees extended
with predicates for equality and disequality between subtrees, and cardinality.Comment: 39 pages, to appear in LMCS journa
Automatic sets of rational numbers
The notion of a k-automatic set of integers is well-studied. We develop a new
notion - the k-automatic set of rational numbers - and prove basic properties
of these sets, including closure properties and decidability.Comment: Previous version appeared in Proc. LATA 2012 conferenc
Descriptional complexity of cellular automata and decidability questions
We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata
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