1,617 research outputs found
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms
The local minimum degree of a graph is the minimum degree that can be reached
by means of local complementation. For any n, there exist graphs of order n
which have a local minimum degree at least 0.189n, or at least 0.110n when
restricted to bipartite graphs. Regarding the upper bound, we show that for any
graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n)
for bipartite graphs, improving the known n/2 upper bound. We also prove that
the local minimum degree is smaller than half of the vertex cover number (up to
a logarithmic term). The local minimum degree problem is NP-Complete and hard
to approximate. We show that this problem, even when restricted to bipartite
graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which
W[1]-hardness is a long standing open question. Finally, we show that the local
minimum degree is computed by a O*(1.938^n)-algorithm, and a
O*(1.466^n)-algorithm for the bipartite graphs
Operations on Automata with All States Final
We study the complexity of basic regular operations on languages represented
by incomplete deterministic or nondeterministic automata, in which all states
are final. Such languages are known to be prefix-closed. We get tight bounds on
both incomplete and nondeterministic state complexity of complement,
intersection, union, concatenation, star, and reversal on prefix-closed
languages.Comment: In Proceedings AFL 2014, arXiv:1405.527
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
Nondeterministic State Complexity for Suffix-Free Regular Languages
We investigate the nondeterministic state complexity of basic operations for
suffix-free regular languages. The nondeterministic state complexity of an
operation is the number of states that are necessary and sufficient in the
worst-case for a minimal nondeterministic finite-state automaton that accepts
the language obtained from the operation. We consider basic operations
(catenation, union, intersection, Kleene star, reversal and complementation)
and establish matching upper and lower bounds for each operation. In the case
of complementation the upper and lower bounds differ by an additive constant of
two.Comment: In Proceedings DCFS 2010, arXiv:1008.127
On the Minimum Degree up to Local Complementation: Bounds and Complexity
The local minimum degree of a graph is the minimum degree reached by means of
a series of local complementations. In this paper, we investigate on this
quantity which plays an important role in quantum computation and quantum error
correcting codes. First, we show that the local minimum degree of the Paley
graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge,
the highest known bound on an explicit family of graphs. Probabilistic methods
allows us to derive the existence of an infinite number of graphs whose local
minimum degree is linear in their order with constant 0.189 for graphs in
general and 0.110 for bipartite graphs. As regards the computational complexity
of the decision problem associated with the local minimum degree, we show that
it is NP-complete and that there exists no k-approximation algorithm for this
problem for any constant k unless P = NP.Comment: 11 page
Quotient Complexity of Regular Languages
The past research on the state complexity of operations on regular languages
is examined, and a new approach based on an old method (derivatives of regular
expressions) is presented. Since state complexity is a property of a language,
it is appropriate to define it in formal-language terms as the number of
distinct quotients of the language, and to call it "quotient complexity". The
problem of finding the quotient complexity of a language f(K,L) is considered,
where K and L are regular languages and f is a regular operation, for example,
union or concatenation. Since quotients can be represented by derivatives, one
can find a formula for the typical quotient of f(K,L) in terms of the quotients
of K and L. To obtain an upper bound on the number of quotients of f(K,L) all
one has to do is count how many such quotients are possible, and this makes
automaton constructions unnecessary. The advantages of this point of view are
illustrated by many examples. Moreover, new general observations are presented
to help in the estimation of the upper bounds on quotient complexity of regular
operations
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