efficient algorithms for membership in boolean hierarchies of regular languages this paper provides efficient algorithms that decide membership for classes of several boolean hierarchies for which efficiency or even decidability were previously not known we develop new forbidden chain characterizations for the single levels of these hierarchies and obtain the following results the classes of the boolean hierarchy over level 1 of the dot depth hierarchy are decidable in nl previously only the decidability was known the same remains true if predicates mod d for fixed d are allowed if modular predicates for arbitrary d are allowed then the classes of the boolean hierarchy over level 1 are decidable for the restricted case of a two letter alphabet the classes of the boolean hierarchy over level 2 of the straubing therien hierarchy are decidable in nl this is the first decidability result for this hierarchy the membership problems for all mentioned boolean hierarchy classes are logspace many one hard for nl the membership problems for quasi aperiodic languages and for d quasi aperiodic languages are logspace many one complete for pspace

nonlinearity of the fuzzy integral we prove that the fuzzy integral has some linearity properties only for small classes of fuzzy measures we also show that an extension of this concept to bounded functions as proposed by kandel 2 5 is not well defined in general

a unified approach to the monotone convergence theorem for nonlinear integrals abstract we present a unified approach to the monotone convergence theorem for nonlinear integrals such as the choquet the sipos the sugeno and the shilkret integral a nonlinear integral may be viewed as a nonlinear functional defined on a set of pairs of a nonadditive measure and a measurable function we thus formulate our general type of monotone convergence theorem for such a functional the key tool is a perturbation of functional that manages not only the monotonicity of the functional but also the small change of the functional value arising as a result of adding small amounts to a measure and a function in the domain of the functional our approach is also applicable to the lebesgue integral when a nonadditive measure is additive

completions of local rings with an isolated singularity abstract it is shown that all equicharacteristic complete local rings can be realized as completions of local rings whose proper localizations are all regular the only restriction in the mixed characteristic case is that the prime integer cannot be a nonzero zerodivisor in any proper localization of the complete ring the constructed examples are unique factorization domains whenever possible and in general are as close to being ufds as the hypothesis will allow

characterization of completions of excellent domains of characteristic zero abstract we show that a complete local ring t containing the integers is the completion of a local excellent integral domain if and only if it is reduced equidimensional and no integer of t is a zero divisor

the symmetric sugeno integral we propose an extension of the sugeno integral for negative numbers in the spirit of the symmetric extension of choquet integral also called sipos integral our framework is purely ordinal since the sugeno integral has its interest when the underlying structure is ordinal we begin by defining negative numbers on a linearly ordered set and we endow this new structure with a suitable algebra very close to the ring of real numbers in a second step we introduce the mobius transform on this new structure lastly we define the symmetric sugeno integral and show its similarity with the symmetric choquet integral

going higher in first order quantifier alternation hierarchies on words we investigate quantifier alternation hierarchies in first order logic on finite words levels in these hierarchies are defined by counting the number of quantifier alternations in formulas we prove that one can decide membership of a regular language in the levels b 2 finite boolean combinations of formulas having only one alternation and 3 formulas having only two alternations and beginning with an existential block our proofs work by considering a deeper problem called separation which once solved for lower levels allows us to solve membership for higher levels

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

descriptional and computational complexity of finite automata a survey finite automata are probably best known for being equivalent to right linear context free grammars and thus for capturing the lowest level of the chomsky hierarchy the family of regular languages over the last half century a vast literature documenting the importance of deterministic nondeterministic and alternating finite automata as an enormously valuable concept has been developed in the present paper we tour a fragment of this literature mostly we discuss developments relevant to finite automata related problems like for example i simulation of and by several types of finite automata ii standard automata problems such as fixed and general membership emptiness universality equivalence and related problems and iii minimization and approximation we thus come across descriptional and computational complexity issues of finite automata we do not prove these results but we merely draw attention to the big picture and some of the main ideas involved

an extension of sugeno integral abstract in this paper we extend the concept of sugeno fuzzy integral from nonnegative fuzzy measurable functions to extended real valued fuzzy measurable functions and discuss the lost genuine properties for this extension several necessary and sufficient conditions of absolute s integrability for extended real valued fuzzy measurable functions are given moreover the space s of all fuzzy measurable functions will be proved to be a pseudo metric space under a necessary and sufficient condition finally as an application of this extension the pettis integral will be established for this kind of fuzzy integral

autocontinuity convergence in measure and convergence in distribution abstract it is shown that the autocontinuity is equivalent to the property that the convergence in measure implies the convergence in distribution this result is applied to denneberg s dominated convergence theorem for the choquet integral

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

the vitali convergence in measure theorem of nonlinear integrals abstract the vitali convergence in measure theorem for the abstract lebesgue integral is fundamental in lebesgue integration theory and yields the bounded convergence theorem and the dominated convergence theorem as its applications in this paper in a unified way using the perturbation method the vitali convergence in measure theorem is established for nonlinear integrals such as the choquet sipos sugeno and shilkret integrals and their symmetric and asymmetric extensions it is derived from the fatou and the reverse fatou type lemmas for perturbative nonlinear integral functionals

complexity of some problems from the theory of automata 1 1 given a finite alphabet l the regular events over x are those accepted by a finite state automaton by kleene s theorem a subset w of s is a regular event if and only if it can be constructed from the finiteword sets by boolean operations together with concatenation and operation in some sense the regular events are quite simple because they are accepted by a machine with no storage capacity nevertheless in recent years much attention has been paid to special subclasses of the class of regular events in this paper we shall be concerned with star free events events of dot depth one and piecewise testable events star free events are constructed like regular events from the finite word sets but with the restriction that the operation is not allowed events of dot depth one and piecewise testable events are star free of a very simple form and will be defined below star free events have been characterized in the work of schiitzenberger 1965 in terms of their syntactic monoid algebraic characterizations of the other two classes have been given simon 1975 knast 1983 from an algorithmic point of view these algebraic characterizations do not yield efficient procedures because computing the syntactic monoid of a regular event given e g by an automaton is obviously time consuming in this paper we investigate the complexity of three problems which we now describe in the style of garey and johnson 1979 we refer the reader to aho hopcroft and ullman 1983 garey and johnson 1979 for standard concepts of complexity theory

languages recognized by finite aperiodic groupoids we study the context free languages recognized by a groupoid g in terms of the algebraic properties of the multiplication monoid m g of g concentrating on the case where m g is group free we show that all regular languages can be recognized by groupoids for which m g is j trivial and that all groupoids for which m g belongs to the larger variety da recognize only regular languages further we give an example of a groupoid such that m g is in the smallest variety outside of da and which recognizes all context free languages not containing the empty word

the bounded convergence in measure theorem for nonlinear integral functionals in this paper we introduce a new notion of the perturbation of nonlinear functionals to formulate a functional form of the convergence theorems for nonlinear integrals in nonadditive measure theory as its direct consequences we obtain the bounded convergence in measure theorems for typical nonlinear integrals which show that the autocontinuity of a nonadditive measure is equivalent to the validity of the bounded convergence in measure theorems for the choquet the sugeno and the shilkret integrals as well as their symmetric and asymmetric extensions

characterization of completions of unique factorization domains it is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field a discrete valuation ring or it has depth at least two and no element of its prime ring is a zerodivisor it is also shown that the normal chain conjecture is false and that there exist local noncatenary ufds

asymptotic structural characteristics of fuzzy measure and their applications abstract in fuzzy measure theory as sugeno s fuzzy measures lose additivity in general the concept almost which is well known in classical measure theory splits into two different concepts almost and pseudo almost in order to replace the additivity it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called waxing and waning and to introduce some new concepts such as autocontinuity converse autocontinuity and pseudo autocontinuity these concepts describe some asymptotic structural characteristics of a fuzzy measure in this paper by means of the asymptotic structural characteristics of fuzzy measure we also give four forms of generalization for both egoroff s theorem riesz s theorem and lebesgue s theorem respectively and prove the almost everywhere pseudo almost everywhere convergence theorem the convergence in measure pseudo in measure theorem of the sequence of fuzzy integrals in the last two theorems the employed conditions are not only sufficient but also necessary

convergence in measure theorems of nonlinear integrals of functions integrable to the pth power abstract one can find a subadditive measure and a sequence f n n n of nonnegative measurable functions converging in measure to such a function f with the property that for any p 1 f n p no longer converges in measure to f p therefore in nonadditive measure theory an additional and intrinsic discussion is needed to prove integral convergence theorems for functions integrable to the pth power the purpose of the paper is to propose a method for automatically deriving pth power versions of convergence in measure theorems of nonlinear integrals from already established ones the proposed method is based on the robustness of some properties of integral functional under the operation f f p raising a nonnegative function f to the pth power

on boolean combinations forming piecewise testable languages abstract a regular language is k piecewise testable k pt if it is a boolean combination of languages of the form l a 1 a 2 a n a 1 a 2 a n where a i and 0 n k given a finite automaton a if the language l a is piecewise testable we want to express it as a boolean combination of languages of the above form the idea is as follows if the language is k pt then there exists a congruence k of finite index such that l a is a finite union of k classes every such class is characterized by an intersection of languages of the from l u for u k and their complements to represent the k classes we make use of the k canonical dfa we identify the states of the k canonical dfa whose union forms the language l a and use them to construct the required boolean combination we study the computational and descriptional complexity of related problems

from cascade decompositions to bit vector algorithms a vector algorithm is an algorithm that applies a bounded number of vector operations to an input vcctor regardless of the length of the input in this paper we describe the links between the existence of vector algorithms and the cascade decompositions of counter free automata we show that any computation that can be carried out with a counter free automaton can be recast as a vector algorithm moreover we show that for a class of automata that is closely related to algorithms in bio computing the complexity of the resulting algorithms is linear in the number of transitions of the original automaton

excellent rings with local generic formal fibers abstract let t m be a complete regular local ring of dimension at least 2 containing the rationals such that the cardinality of the residue field t m is at least the cardinality of the real numbers suppose p m is a prime ideal of t we construct an excellent regular local ring a such that the completion of a is t and the generic formal fiber of a is local this means that the ring t a k is a local ring where k is the quotient field of a with p a k its maximal ideal in addition if q is a prime ideal of t with q a p 0 then q pt

some complexity results for polynomial rational expressions it is known that any languages of level 3 2 of the straubing therien hierarchy can be written as a polynomial expression that is a finite union of languages of the form a0 b1a 1 b kak where the ai and bi are subsets of the alphabet in this paper we prove that such a polynomial expression for a 3 2 level language can be of exponential size more precisely we exhibit an n state minimal automaton recognizing a level 3 2 language for which the shortest polynomial expresion has exponential size in n

a polynomial time algorithm for the local testability problem of deterministic finite automata the local testability problem of deterministic finite automata is investigated a locally testable language is a language with the property that for some nonnegative integer k whether or not a word w is in the language depends on 1 the prefix and suffix of w of length k and 2 the set of substrings of w length k 1 without regard to the order in which these substrings occur the local testability problem is given a deterministic finite automation to decide whether or not it accepts a locally testable language the authors present an o n sup 2 time algorithm for the local testability problem based on two simple properties that characterize locally testable automata

on the convergence theorems of generalized fuzzy integral sequence in this paper we give a counterexample showing that two convergence theorems of generalized fuzzy integrals given by wu et al fuzzy sets and systems 70 1995 75 87 is not valid and modify them to the right forms

characterizations of some classes of regular events abstract we study two special classes of regular events the piecewise testable events and the events of dot depth one several characterizations of these events are given especially in terms of their minimal automaton

weak convergence of nonadditive measures based on nonlinear integral functionals abstract in this paper we formulate a general portmanteau theorem for a perturbative nonlinear integral functional and discuss the uniformity of weak convergence of nonadditive measures based on such a functional as their direct consequences it turns out that levy convergence of nonadditive measures coincides with every one of three types of weak convergence that is weak choquet weak sugeno and weak shilkret convergence and they are uniform on every bounded subset of lipschitz functions those results are applied when discussing the metrizability of the levy topology on the space of nonadditive measures and defining the fortet mourier type metrics on a uniformly equi autocontinuous set of nonadditive measures

novel survival functions based on conditional aggregation operators abstract in this paper we define a novel survival function motivated by real life problems which generalizes the super level measure introduced by do and thiele 2015 this concept is based on conditional aggregation operators extending the definition of aggregation operators introduced by calvo et al 2002 for all bounded measurable functions and not only for finite sequences some basic properties and several examples of conditional aggregation operators are presented using the novel survival function the choquet stieltjes functional is introduced and the conditions are indicated under which this functional can be called an integral the new functional generalizes several known integrals including the choquet stieltjes integral as well as choquet integral with respect to level dependent capacity introduced by greco et al 2011

pspace complete problems for subgroups of free groups and inverse finite automata we investigate the complexity of algorithmic problems on finitely generated subgroups of free groups margolis and meakin showed how a finite monoid synt h can be canonically and effectively associated with such a subgroup h we show that h is pure that is closed under radical if and only if synt h is aperiodic we also show that testing for this property of h is pspace complete in the process we show that certain problems about finite automata which are pspace complete in general remain pspace complete when restricted to injective and inverse automata with single accept state whereas they are known to be in nc for permutation automata with single accept state

some results on the generalized star height problem abstract we prove some results related to the generalized star height problem in this problem as opposed to the restricted star height problem complementation is considered as a basic operator we first show that the class of languages of star height n is closed under certain operations left and right quotients inverse alphabetic morphisms injective star free substitutions it is known that languages recognized by a commutative group are of star height 1 we extend this result to nilpotent groups of class 2 and to the groups that divide a semidirect product of a commutative group by z 2 z n in the same direction we show that one of the languages that were conjectured to be of star height 2 during the past ten years is in fact of star height 1 next we show that if a rational language l is recognized by a monoid of the variety generated by wreath products of the form m g n where m and n are aperiodic monoids and g is a commutative group the l is of star height 1 finally we show that every rational language is the inverse image under some morphism between free monoids of a language of resticted star height 1