4,556 research outputs found
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
Most Complex Regular Right-Ideal Languages
A right ideal is a language L over an alphabet A that satisfies L = LA*. We
show that there exists a stream (sequence) (R_n : n \ge 3) of regular right
ideal languages, where R_n has n left quotients and is most complex under the
following measures of complexity: the state complexities of the left quotients,
the number of atoms (intersections of complemented and uncomplemented left
quotients), the state complexities of the atoms, the size of the syntactic
semigroup, the state complexities of the operations of reversal, star, and
product, and the state complexities of all binary boolean operations. In that
sense, this stream of right ideals is a universal witness.Comment: 19 pages, 4 figures, 1 tabl
A New Technique for Reachability of States in Concatenation Automata
We present a new technique for demonstrating the reachability of states in
deterministic finite automata representing the concatenation of two languages.
Such demonstrations are a necessary step in establishing the state complexity
of the concatenation of two languages, and thus in establishing the state
complexity of concatenation as an operation. Typically, ad-hoc induction
arguments are used to show particular states are reachable in concatenation
automata. We prove some results that seem to capture the essence of many of
these induction arguments. Using these results, reachability proofs in
concatenation automata can often be done more simply and without using
induction directly.Comment: 23 pages, 1 table. Added missing affiliation/funding informatio
Large Aperiodic Semigroups
The syntactic complexity of a regular language is the size of its syntactic
semigroup. This semigroup is isomorphic to the transition semigroup of the
minimal deterministic finite automaton accepting the language, that is, to the
semigroup generated by transformations induced by non-empty words on the set of
states of the automaton. In this paper we search for the largest syntactic
semigroup of a star-free language having left quotients; equivalently, we
look for the largest transition semigroup of an aperiodic finite automaton with
states.
We introduce two new aperiodic transition semigroups. The first is generated
by transformations that change only one state; we call such transformations and
resulting semigroups unitary. In particular, we study complete unitary
semigroups which have a special structure, and we show that each maximal
unitary semigroup is complete. For there exists a complete unitary
semigroup that is larger than any aperiodic semigroup known to date.
We then present even larger aperiodic semigroups, generated by
transformations that map a non-empty subset of states to a single state; we
call such transformations and semigroups semiconstant. In particular, we
examine semiconstant tree semigroups which have a structure based on full
binary trees. The semiconstant tree semigroups are at present the best
candidates for largest aperiodic semigroups.
We also prove that is an upper bound on the state complexity of
reversal of star-free languages, and resolve an open problem about a special
case of state complexity of concatenation of star-free languages.Comment: 22 pages, 1 figure, 2 table
Most Complex Non-Returning Regular Languages
A regular language is non-returning if in the minimal deterministic
finite automaton accepting it there are no transitions into the initial state.
Eom, Han and Jir\'askov\'a derived upper bounds on the state complexity of
boolean operations and Kleene star, and proved that these bounds are tight
using two different binary witnesses. They derived upper bounds for
concatenation and reversal using three different ternary witnesses. These five
witnesses use a total of six different transformations. We show that for each
there exists a ternary witness of state complexity that meets the
bound for reversal and that at least three letters are needed to meet this
bound. Moreover, the restrictions of this witness to binary alphabets meet the
bounds for product, star, and boolean operations. We also derive tight upper
bounds on the state complexity of binary operations that take arguments with
different alphabets. We prove that the maximal syntactic semigroup of a
non-returning language has elements and requires at least
generators. We find the maximal state complexities of atoms of
non-returning languages. Finally, we show that there exists a most complex
non-returning language that meets the bounds for all these complexity measures.Comment: 22 pages, 6 figure
Exchange Rate Variability and Foreign Direct Investment - Consequences of EMU Enlargement
The aim of the paper is to analyze theoretically and empirically the likely impact of the reduction in exchange rate uncertainty, due to the EMU accession, on the intensity of FDI inflow into candidate countries. Theoretical models give an ambiguous picture of how exchange rate uncertainty and volatility affect direction and magnitude of FDI inflows. The main contribution of this paper is in finding that exchange rate uncertainty and volatility may negatively influence the decision to locate investment in transition and accession countries. Nominal exchange rate uncertainty seems to particularly hamper FDI inflows in accession countries. The key finding of this paper is that euro adoption is likely to exert a positive influence on FDI inflows in accession countries.foreign direct investment, exchange rate uncertainty and volatility, transition, euro adoption
Universal Witnesses for State Complexity of Basic Operations Combined with Reversal
We study the state complexity of boolean operations, concatenation and star
with one or two of the argument languages reversed. We derive tight upper
bounds for the symmetric differences and differences of such languages. We
prove that the previously discovered bounds for union, intersection,
concatenation and star of such languages can all be met by the recently
introduced universal witnesses and their variants.Comment: 18 pages, 8 figures. LNCS forma
Maximally Atomic Languages
The atoms of a regular language are non-empty intersections of complemented
and uncomplemented quotients of the language. Tight upper bounds on the number
of atoms of a language and on the quotient complexities of atoms are known. We
introduce a new class of regular languages, called the maximally atomic
languages, consisting of all languages meeting these bounds. We prove the
following result: If L is a regular language of quotient complexity n and G is
the subgroup of permutations in the transition semigroup T of the minimal DFA
of L, then L is maximally atomic if and only if G is transitive on k-subsets of
1,...,n for 0 <= k <= n and T contains a transformation of rank n-1.Comment: In Proceedings AFL 2014, arXiv:1405.527
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