170 research outputs found
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
State Complexity of Regular Tree Languages for Tree Matching
We study the state complexity of regular tree languages for tree matching problem. Given a tree t and a set of pattern trees L, we can decide whether or not there exists a subtree occurrence of trees in L from the tree t by considering the new language L′ which accepts all trees containing trees in L as subtrees. We consider the case when we are given a set of pattern trees as a regular tree language and investigate the state complexity. Based on the sequential and parallel tree concatenation, we define three types of tree languages for deciding the existence of different types of subtree occurrences. We also study the deterministic top-down state complexity of path-closed languages for the same problem.</jats:p
State complexity of Kleene-star operations on regulat tree languages
The concatenation of trees can be defined either as a sequential or a parallel operation, and the corresponding iterated operation gives an extension of Kleene-star to tree languages. Since the sequential tree concatenation is not associative, we get two essentially different iterated sequential concatenation operations that we call the bottom-up star and top-down star operation, respectively. We establish that the worst-case state complexity of bottom-up star is (n + 3/2) · 2 n−1. The bound differs by an order of magnitude from the corresponding result for string languages. The state complexity of top-down star is similar as in the string case. We consider also the state complexity of the star of the concatenation of a regular tree language with the set of all trees
Ambiguity, nondeterminism and state complexity of finite automata
The degree of ambiguity counts the number of accepting computations of a nondeterministic finite automaton (NFA) on a given input. Alternatively, the nondeterminism of an NFA can be measured by counting the amount of guessing in a single computation or the number of leaves of the computation tree on a given input. This paper surveys work on the degree of ambiguity and on various nondeterminism measures for finite automata. In particular, we focus on state complexity comparisons between NFAs with quantified ambiguity or nondeterminism
P Systems with Minimal Left and Right Insertion and Deletion
In this article we investigate the operations of insertion and deletion performed
at the ends of a string. We show that using these operations in a P systems
framework (which corresponds to using specific variants of graph control), computational
completeness can even be achieved with the operations of left and right insertion and
deletion of only one symbol
First Steps Towards a Geometry of Computation
We introduce a geometrical setting which seems promising for the study
of computation in multiset rewriting systems, but could also be applied to register machines and other models of computation. This approach will be applied here to membrane
systems (also known as P systems) without dynamical membrane creation. We discuss
the role of maximum parallelism and further simplify our model by considering only one
membrane and sequential application of rules, thereby arriving at asynchronous multiset
rewriting systems (AMR systems). Considering only one membrane is no restriction, as
each static membrane system has an equivalent AMR system. It is further shown that
AMR systems without a priority relation on the rules are equivalent to Petri Nets. For
these systems we introduce the notion of asymptotically exact computation, which allows
for stochastic appearance checking in a priori bounded (for some complexity measure)
computations. The geometrical analogy in the lattice Nd0
; d 2 N, is developed, in which a
computation corresponds to a trajectory of a random walk on the directed graph induced
by the possible rule applications. Eventually this leads to symbolic dynamics on the partition generated by shifted positive cones C+
p , p 2 Nd0
, which are associated with the
rewriting rules, and their intersections. Complexity measures are introduced and we consider non-halting, loop-free computations and the conditions imposed on the rewriting
rules. Eventually, two models of information processing, control by demand and control by
availability are discussed and we end with a discussion of possible future developments
P Systems with Minimal Left and Right Insertion and Deletion
Summary. In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol.
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