173,831 research outputs found
Splicing Systems from Past to Future: Old and New Challenges
A splicing system is a formal model of a recombinant behaviour of sets of
double stranded DNA molecules when acted on by restriction enzymes and ligase.
In this survey we will concentrate on a specific behaviour of a type of
splicing systems, introduced by P\u{a}un and subsequently developed by many
researchers in both linear and circular case of splicing definition. In
particular, we will present recent results on this topic and how they stimulate
new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in
Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian
Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other
author
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
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
Groups with poly-context-free word problem
We consider the class of groups whose word problem is poly-context-free; that
is, an intersection of finitely many context-free languages. We show that any
group which is virtually a finitely generated subgroup of a direct product of
free groups has poly-context-free word problem, and conjecture that the
converse also holds. We prove our conjecture for several classes of soluble
groups, including metabelian groups and torsion-free soluble groups, and
present progress towards resolving the conjecture for soluble groups in
general. Some of the techniques introduced for proving languages not to be
poly-context-free may be of independent interest.Comment: 38 pages, no figure
On periodic points of free inverse monoid endomorphisms
It is proved that the periodic point submonoid of a free inverse monoid
endomorphism is always finitely generated. Using Chomsky's hierarchy of
languages, we prove that the fixed point submonoid of an endomorphism of a free
inverse monoid can be represented by a context-sensitive language but, in
general, it cannot be represented by a context-free language.Comment: 18 page
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