87,235 research outputs found
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
Operational State Complexity under Parikh Equivalence
We investigate, under Parikh equivalence, the state complexity of some language operations which preserve regularity. For union, concatenation, Kleene star, complement, intersection, shue, and reversal, we obtain a polynomial state complexity over any xed alphabet, in contrast to the intrinsic exponential state complexity of some of these operations in the classical version. For projection we prove a superpolynomial state complexity, which is lower than the exponential one of the corresponding classical operation. We also prove that for each two deterministic automata A and B it is possible to obtain a deterministic automaton with a polynomial number of states whose accepted language has as Parikh image the intersection of the Parikh images of the languages accepted by A and B
Universal Disjunctive Concatenation and Star
Two language operations that can be expressed by suitably combining complement with concatenation and star, respectively, are introduced. The state complexity of those operations on regular languages is investigated. In the deterministic case, optimal exponential state gaps are proved for both operations. In the nondeterministic case, for one operation an optimal exponential gap is also proved, while for the other operation an exponential upper bound is obtained. (c) Springer International Publishing Switzerland 2015
Quotient Complexity Of Closed Languages
The final publication is available at Springer via http://dx.doi.org/10.1007/s00224-013-9515-7A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in an analogous way, where by factor we mean contiguous subsequence, and by subword we mean scattered subsequence. We study the state complexity (which we prefer to call quotient complexity) of operations on prefix-, suffix-, factor-, and subword-closed languages. We find tight upper bounds on the complexity of the subword-closure of arbitrary languages, and on the complexity of boolean operations, concatenation, star, and reversal in each of the four classes of closed languages. We show that repeated applications of positive closure and complement to a closed language result in at most four distinct languages, while Kleene closure and complement give at most eight.Natural Sciences and Engineering Research Council of Canada [OGP0000871]VEGA grant [2/0183/11][APVV-0035-10
On the Structure and Complexity of Rational Sets of Regular Languages
In a recent thread of papers, we have introduced FQL, a precise specification
language for test coverage, and developed the test case generation engine
FShell for ANSI C. In essence, an FQL test specification amounts to a set of
regular languages, each of which has to be matched by at least one test
execution. To describe such sets of regular languages, the FQL semantics uses
an automata-theoretic concept known as rational sets of regular languages
(RSRLs). RSRLs are automata whose alphabet consists of regular expressions.
Thus, the language accepted by the automaton is a set of regular expressions.
In this paper, we study RSRLs from a theoretic point of view. More
specifically, we analyze RSRL closure properties under common set theoretic
operations, and the complexity of membership checking, i.e., whether a regular
language is an element of a RSRL. For all questions we investigate both the
general case and the case of finite sets of regular languages. Although a few
properties are left as open problems, the paper provides a systematic semantic
foundation for the test specification language FQL
Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages
A language over an alphabet is suffix-convex if, for any words
, whenever and are in , then so is .
Suffix-convex languages include three special cases: left-ideal, suffix-closed,
and suffix-free languages. We examine complexity properties of these three
special classes of suffix-convex regular languages. In particular, we study the
quotient/state complexity of boolean operations, product (concatenation), star,
and reversal on these languages, as well as the size of their syntactic
semigroups, and the quotient complexity of their atoms.Comment: 20 pages, 11 figures, 1 table. arXiv admin note: text overlap with
arXiv:1605.0669
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