4,990 research outputs found
Splicing representations of strictly locally testable languages
AbstractThe relationship between the family SH of simple splicing languages, which was recently introduced by Mateescu et al. and the family SLT of strictly locally testable languages is clarified by establishing an ascending hierarchy of families {SiH: i⩾ − 1} of splicing languages for which SH = S1H and the union of the families is the family SLT. A procedure is given which, for an arbitrary regular language L, determines whether L is in SLT and, when L is in SLT, specifies constructively the smallest family in the hierarchy to which L belongs. Examples are given of sets of restriction enzymes for which the action on DNA molecules is naturally represented by splicing systems of the types discussed
Strictly Locally Testable and Resources Restricted Control Languages in Tree-Controlled Grammars
Tree-controlled grammars are context-free grammars where the derivation
process is controlled in such a way that every word on a level of the
derivation tree must belong to a certain control language. We investigate the
generative capacity of such tree-controlled grammars where the control
languages are special regular sets, especially strictly locally testable
languages or languages restricted by resources of the generation (number of
non-terminal symbols or production rules) or acceptance (number of states).
Furthermore, the set theoretic inclusion relations of these subregular language
families themselves are studied.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Higher-Order Operator Precedence Languages
Floyd's Operator Precedence (OP) languages are a deterministic context-free
family having many desirable properties. They are locally and parallely
parsable, and languages having a compatible structure are closed under Boolean
operations, concatenation and star; they properly include the family of Visibly
Pushdown (or Input Driven) languages. OP languages are based on three relations
between any two consecutive terminal symbols, which assign syntax structure to
words. We extend such relations to k-tuples of consecutive terminal symbols, by
using the model of strictly locally testable regular languages of order k at
least 3. The new corresponding class of Higher-order Operator Precedence
languages (HOP) properly includes the OP languages, and it is still included in
the deterministic (also in reverse) context free family. We prove Boolean
closure for each subfamily of structurally compatible HOP languages. In each
subfamily, the top language is called max-language. We show that such languages
are defined by a simple cancellation rule and we prove several properties, in
particular that max-languages make an infinite hierarchy ordered by parameter
k. HOP languages are a candidate for replacing OP languages in the various
applications where they have have been successful though sometimes too
restrictive.Comment: In Proceedings AFL 2017, arXiv:1708.0622
A Characterization for Decidable Separability by Piecewise Testable Languages
The separability problem for word languages of a class by
languages of a class asks, for two given languages and
from , whether there exists a language from that
includes and excludes , that is, and . In this work, we assume some mild closure properties for
and study for which such classes separability by a piecewise
testable language (PTL) is decidable. We characterize these classes in terms of
decidability of (two variants of) an unboundedness problem. From this, we
deduce that separability by PTL is decidable for a number of language classes,
such as the context-free languages and languages of labeled vector addition
systems. Furthermore, it follows that separability by PTL is decidable if and
only if one can compute for any language of the class its downward closure wrt.
the scattered substring ordering (i.e., if the set of scattered substrings of
any language of the class is effectively regular).
The obtained decidability results contrast some undecidability results. In
fact, for all (non-regular) language classes that we present as examples with
decidable separability, it is undecidable whether a given language is a PTL
itself.
Our characterization involves a result of independent interest, which states
that for any kind of languages and , non-separability by PTL is
equivalent to the existence of common patterns in and
Conditional Lindenmayer systems with subregular conditions : the extended case
We study the generative power of extended conditional Lindenmayer systems where the conditions are finite, monoidal, combinational, definite, nilpotent, strictly locally (k)-testable, commutative, circular, suffix-closed, starfree, and union-free regular languages. The results correspond to those obtained for conditional context-free languages
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