fine hierarchy of regular ω languages by applying descriptive set theory we get several facts on the fine structure of regular languages considered by k wagner we present quite different shorter proofs for main his results and get new results our description of the fine structure is new very clear and automata free we prove also a closure property of the fine structure under boolean operations our results demonstrate deep interconnections between descriptive set theory and theory of languages

exact simultaneous confidence intervals for pairwise comparisons of three normal means abstract the problem of simultaneously estimating the pairwise differences of means of three independent normal populations with equal variances is considered a computational method involving a bivariate t density is used to form confidence intervals with simultaneous coverage probability equal to 1 a for equal sample sizes the method is the tukey studentized range procedure with unequal sample sizes the method is superior to the various generalized tukey methods a table of probability points is presented for small sample sizes a large sample approximation based on the bivariate normal and studentized range distributions is given

the monadic second order logic of graphs ix machines and their behaviours abstract we establish that every monadic second order property of the behaviour of a machine transition systems and tree automata are typical examples of machines is a monadic second order property of the machine itself in this way we clarify the distinction between dynamic properties of machines i e properties of their behaviours and their static properties i e properties of the graphs or relational structures representing them it is important for program verification that the dynamic properties that one wants to verify can be formulated statically in the simplest possible way as a corollary of our main result we also obtain that the monadic theory of an algebraic tree is decidable

testing and selecting for equivalence with respect to a control abstract the problem of equivalence assessment of several treatments with a control is considered the first approach uses a hypothesis testing formulation in which the alternative states global equivalence with respect to a family of distributions with location parameter a test based on a two sided many one statistic is proposed least favorable parameter configuration results are presented as being necessary to evaluate critical values and to determine sample sizes implied by certain power requirements when planning experiments the second approach concerns a stepwise selection procedure the goal is to select a subset of treatments containing all those actually equivalent to the control in the absence of global equivalence the normal case is dealt with in detail for randomized block designs as well as for one way layouts concerning the test problem optimal allocations of total sample sizes are determined to guarantee specified power requirements for the one way layout

multiple testing of general contrasts powerful improvements are possible for multiple testing procedures when the hypotheses are logically related closed testing with exhaustive tests provides a unifying framework for developing such procedures but can be computationally difficult and can be nonmonotonic in p values royen introduced a truncated closed testing method for the case of all pairwise comparisons in the analysis of variance that is monotonic in p values shaffer developed a similar truncated procedure for more general comparisons but using bonferroni tests rather than exhaustive tests and westfall extended shaffer s method to allow exhaustive tests this article extends royen s method to general contrasts and proves that it is equivalent to the extended shaffer procedure for k contrasts the method generally requires evaluation of o 2k critical values that correspond to subset intersection hypotheses and is computationally infeasible for large k the set of intersections is represented using a tree structure and a

fundamental properties of infinite trees infinite trees naturally arise in the formalization and the study of the semantics of programming languages this paper investigates some of their combinatorial and algebraic properties that are especially relevant to semantics

simultaneous confidence intervals for pairwise multiple comparisons in a two way unbalanced design turkey s 1953 the problem of multiple comparisons unpublished report princeton university procedure is widely used for pairwise multiple comparisons in one way anova it provides exact simultaneous pairwise confidence intervals spci for balanced designs and conservative spci for unbalanced designs in this paper we will extend turkey s procedure to two way unbalanced designs both the exact and the conservative methods will be introduced the application of the new procedure is illustrated with sample data from two experiments

computations by fly automata beyond monadic second order logic parameterized algorithms based on automata infinite automata computing their transitions problems described in monadic second order logic counting and other problems not expressible in monadic second order logic the validity of a monadic second order ms expressible property can be checked in linear time on graphs of bounded tree width or clique width given with appropriate decompositions this result is proved by constructing from the ms sentence expressing the property and an integer that bounds the tree width or clique width of the input graph a finite automaton intended to run bottom up on the algebraic term representing a decomposition of the input graph as we cannot construct practically the transition tables of these automata because they are huge we use fly automata whose states and transitions are computed on the fly only when needed for a particular input furthermore we allow infinite sets of states and we equip automata with output functions thus they can check properties that are not ms expressible and compute values for example the number of p colorings of a graph we obtain xp and fpt graph algorithms parameterized by tree width or clique width we show how to construct easily such algorithms by combining predefined automata for basic functions and properties these combinations reflect the structure of the ms formula that specifies the property to check or the function to compute

fine hierarchies and m reducibilities in theoretical computer science this is a survey of results about versions of fine hierarchies and many one reducibilities that appear in different parts of theoretical computer science these notions and related techniques play a crucial role in understanding complexity of finite and infinite computations we try not only to present the corresponding notions and facts from the particular fields but also to identify the unifying notions techniques and ideas

counting modulo quantifiers on finite structures we give a combinatorial method for proving elementary equivalence in first order logic fo with counting modulo n quantifiers dn inexpressibility results for fo dn with built in linear order are also considered for instance the class of linear orders of length divisible by n 1 cannot be expressed in fo dn using this result we prove that comparing cardinalities or connectivity of ordered graphs are not definable in fo dn we also show that the height of complete n ary trees cannot be expressed in fo dn with linear order interpreting the predicate y nx as a complete n ary tree we show that the predicate y px cannot be defined in fo dn with linear order whenever p has a prime factor that does not divide n this solves the problem raised by niwi ski and stolboushkin lics 93 we also discuss a connection between our results and the well known open problem in circuit complexity theory whether acc nc1

an improved gt2 method for simultaneous confidence intervals on pairwise differences the problem of pairwise comparisons of three parameters is considered it is assumed that a set of unbiased estimators of these parameters has a trivariate normal distribution with covariance matrix 2 b where b is a known positive definite matrix a probability inequality sharper than that used by hochberg 1974 is discussed based on this inequality it is possible to achieve simultaneous confidence intervals uniformly shorter than those arising from the gt2 method these new intervals are also generally shorter than the intervals arising from scheffe s method and from the bonferroni inequality in addition these new intervals are at times shorter than those from kramer s method when the latter method is appropriate

structural properties of context free sets of graphs generated by vertex replacement abstract we establish that a vertex replacement set of graphs i e a set of graphs generated by a c ednce or equivalently by a separated handle rewriting graph grammar is hyperedge replacement i e is generated by a hyperedge replacement graph grammar iff its graphs do not contain arbitrary large complete bipartite graphs kn n as subgraphs another equivalent condition is that its graphs have a number of edges that is linearly bounded in terms of the number of vertices these properties are decidable by means of an appropriate extension of the theorem by parikh that characterizes the commutative images of context free languages we extend these results to hypergraphs

pairwise comparisons of generally correlated means abstract a commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means i 1 i k for certain experimental designs one way to do this the t method proposed by tukey 1953 constructs simultaneous confidence intervals for all pairwise differences of the treatment means i j 1 i j k i j the joint confidence level of these confidence intervals however depends in a very complicated fashion on the covariance structure of the treatment mean estimates i and therefore for designs where the covariance structure is not simple the joint confidence level is not readily apparent in general this is the case for any unbalanced design or for designs in which the treatment mean estimates i have unequal correlations tukey conjectured in 1953 that whatever the correlation structure of the treatment mean estimates i the t method would always provide a conservative set of confidence intervals that is that th

simultaneous estimation and prediction using the expected coverage measure criterion on utilise des methodes d invariance pour construire des procedures minimax dans les modeles lineaires multivariables

asynchronous mappings and asynchronous cellular automata the aim of this paper is the study of asynchronous automata a special kind of automata which encode the independency relation between actions and which enable their concurrent execution these automata introduced by zielonka rairo inform theor appl 21 99 135 1987 constitute a natural extension of finite automata to the case of asynchronous parallelism their behaviour is described by trace languages subsets of partially commutative monoids the main result concerning this class of automata states that they accept exactly all recognizable trace languages in this paper we give new improved constructions of asynchronous automata in the final part of the paper we present a distributed system of messages with bounded time stamps based on asynchronous automata

a note on the problem of reporting maximal cliques reporting the maximal cliques of a graph is a fundamental problem arising in many areas this note bridges the gap between three papers addressing this problem the original paper of bron kerbosh c bron j kerbosch algorithm 457 finding all cliques of an undirected graph communication of acm 16 9 1973 575 577 and two papers recently published in tcs namely that of tomita et al tomita a tanaka h takahashi the worst case time complexity for generating all maximal cliques and computational experiments theoretical computer science 363 1 2006 28 42 and that of koch i koch fundamental study enumerating all connected maximal common subgraphs in two graphs theoretical computer science 250 1 2 2001 1 30 in particular we show that the strategy of tomita et al is a simple modification of the bron kerbosch algorithm based on an un exploited observation raised in koch s paper

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

john w tukey s contributions to multiple comparisons this article provides a historical overview of the philosophical theoretical and practical contributions made by john tukey to the field of simultaneous inference his early work culminating in the monograph the problem of multiple comparisons established him as one of the pioneers in the field investing it with both academic respectability and a focus on practical problems for many years afterward tukey only published sporadically in the area but remained convinced that multiplicity issues were of fundamental importance during the last decade of his life tukey again devoted substantial attention to multiplicity experimenting with different graphical representations of multiple comparison procedures and exploring the implications of new approaches to controlling family wise error rates he leaves a rich legacy that should engage and inspire statisticians for many years to come

the kolmogorov complexity of infinite words we present a brief survey of results on relations between the kolmogorov complexity of infinite strings and several measures of information content dimensions known from dimension theory information theory or fractal geometry special emphasis is placed on bounds on the complexity of strings in constructively given subsets of the cantor space finally we compare the kolmogorov complexity to the subword complexity of infinite strings

a logical approach of petri net languages abstract for languages recognized by finite automata we dispose of two formalisms regular expressions kleene 1956 and logical formulas buchi 1960 in the case of petri net languages there is no formalism like regular expressions in this paper we give a buchi like theorem which characterizes petri net languages in terms of second order logical formulas this characterization has two advantages 1 it situates exactly the power of petri nets with respect to finite automata roughly speaking petri nets are finite automata plus the ability of testing if a string of parenthesis is well formed in this paper parenthesis always means the usual one sort of parentheses 2 given a language it enables us to easily prove that it is a petri net language in addition we prove that petri net languages and deadlock languages coincide

analytic models and ambiguity of context free languages we establish that several classical context free languages are inherently ambiguous by proving that their counting generating functions when considered as analytic functions exhibit some characteristic form of transcendental behaviour to that purpose we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages in particular the paper contains a general density theorem for unambiguous context free languages

optimum partition procedures for separating good and bad treatments abstract this article considers partitioning a given set of competing treatments into two subsets with the purpose of separating good and bad treatments the qualities good and bad are defined in terms of the parameter vector of the underlying distribution family regarding the probability of an incorrect partition within the class of so called natural procedures minimax solutions are derived under suitable distributional assumptions these results extend previous investigations to the larger family of quasi concave distributions it is shown that the multivariate noncentral t distribution with v degrees of freedom is 1 v concave and hence quasi concave thus the unknown variance case in a normal distribution setup is covered as a special application specifically for partitioning with respect to a control the presented minimax results are used in the unknown variance case to determine optimal allocations of total sample sizes that guarantee a correct partition at a preassigned confidence lev

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

wadge hierarchy of omega context free languages abstract the main result of this paper is that the length of the wadge hierarchy of omega context free languages is greater than the cantor ordinal e 0 and the same result holds for the conciliating wadge hierarchy defined by duparc j symbolic logic to appear of infinitary context free languages studied by beauquier ph d thesis universite paris 7 1984 in the course of our proof we get results on the wadge hierarchy of iterated counter languages which we define as an extension of classical finitary iterated counter languages to languages

locally finite languages we investigate properties of locally finite languages introduced by ressayre j symbolic logic 53 4 1988 1009 1026 these languages are defined by locally finite sentences and generalize languages recognized by automata or defined by monadic second order sentences we give many examples showing that numerous context free languages are locally finite then we study closure properties of the family loc of locally finite languages and show that most undecidability results that hold for context free languages may be extended to locally finite languages in a second part we consider an extension of these languages to infinite and transfinite length words we prove that each language which is recognized by a buchi automaton where is an ordinal and is defined by a locally finite sentence this result combined with a preceding one of finkel and ressayre j symbolic logic 61 2 1996 563 585 provides a generalization of buchi s result about decidability of monadic second order theory of the structure

regular sets over extended tree structures we investigate notions of decidability and definability for the monadic second order logic over labeled tree structures and its relations with finite automata using oracles to test input prefixes a general framework is defined allowing to transfer some mso properties from a graph structure to a labeled tree structure transferred properties are the decidability of sentences and the existence of a definable model for every satisfiable formula a class of finite automata with prefix oracles is also defined recognizing exactly languages defined by mso formulas in any labeled tree structure applying these results the well known equivalence between languages recognized by finite automata sets of vertices mso definable in a tree structure and sets of pushdown contexts generated by pushdown automata is extended to k iterated pushdown automata

simultaneous confidence bands for a percentile hyper plane with covariates constrained in a restricted range abstract a simultaneous confidence band provides useful information about the plausible range of the unknown regression model in several recent papers confidence bands have been used for various inferential purposes see for example liu et al 2004 2005 2009 2010 2012 2014 liu and hayter 2007 1 liu and lin 2009 piegorsch et al 2005 han et al 2015 and zhou 2017 the construction of simultaneous confidence bands has a long history going back to working and hotelling 1929 2 and is often difficult when the region over which a confidence band is required is restricted and the number of predictor variables is greater than one in this paper we have developed methods to construct simultaneous confidence bands for a percentile hyper plane these methods allow us to construct the bands over arbitrary intervals either finite or infinite they also allow us to construct the type i and type ii bands in order to get an idea of the efficiency of these bands we have also developed the confidence sets for the bands and have compared the bands under the minimum volume confidence set optimality criterion the proposed methods are illustrated by an example

the worst case time complexity for generating all maximal cliques and computational experiments we present a depth first search algorithm for generating all maximal cliques of an undirected graph in which pruning methods are employed as in the bron kerbosch algorithm all the maximal cliques generated are output in a tree like form subsequently we prove that its worst case time complexity is o 3n 3 for an n vertex graph this is optimal as a function of n since there exist up to 3n 3 maximal cliques in an n vertex graph the algorithm is also demonstrated to run very fast in practice by computational experiments

on omega context free languages which are borel sets of infinite rank this paper is a continuation of the study of topological properties of omega context free languages cfl we proved in topological properties of omega context free languages theoretical computer science 262 1 2 2001 669 697 that the class of cfl exhausts the finite ranks of the borel hierarchy and in borel hierarchy and omega context free languages theoretical computer science to appear that there exist some cfl which are analytic but non borel sets we prove here that there exist some omega context free languages which are borel sets of infinite but not finite rank giving additional answer to questions of lescow and thomas logical specifications of infinite computations in a decade of concurrency j w de bakker et al eds springer lncs 803 1994 583 621

a multiple comparisons procedure for use in conjunction with the benard van elteren test summary the benard van elteren test statistic is a generalization of the friedman test statistic that permits multiple and unequal replicates per treatment per block a multiple comparisons procedure for pairwise comparisons of treatments is developed for use in conjunction with the benard van elteren test this procedure is applied to an example arising from a clinical trial sufficient conditions for use of this multiple comparisons procedure are given with examples of designs for which these conditions are met this multiple comparisons procedure is shown to be identical to a procedure developed by nemenyi unpublished doctoral thesis princeton university 1963 presented by hollander and wolfe 1973 nonparametric statistical methods new york wiley for the randomized complete block design with one replicate per treatment per block and to a procedure given by campbell 1980 in proceedings of the american statistical association section on statistical education 24 27 for the balanced incomplete block design

the hausdorff kuratowski hierarchy of ω regular languages and a hierarchy of muller automata given a finite alphabet we give a simple characterization of those g subsets of which are deterministic regular i e accepted by buchi automata over and then characterize the regular languages in terms of these rational g sets our characterization yields a hierarchy of regular languages similar to the classical difference hierarchy of hausdorff and kuratowski for 03 sets i e the class of sets which are both f and g we then prove that the hausdorff kuratowski difference hierarchy of 03 when restricted to regular languages coincides with our hierarchy we obtain this by showing that if an regular language k can be separated from another regular language l by the union of alternate differences of a decreasing sequence of g sets of length n then there is a decreasing sequence of length n of rational g sets such that the union of alternate differences separates k from l our results not only generalize a result of landweber 1969 but also yield an effective procedure for determining the complexity of a given muller automaton we also show that our hierarchy does not collapse thus giving a fine classification of regular languages and of muller automata

trees grids and mso decidability from graphs to matroids monadic second order mso logic has proved to be a useful tool in many areas of application reaching flom decidability and complexity to picture processing correctness of programs and parallel processes to characterize the structural borderline between decidability and undecidability is a classical research problem here this problem is related to questions in computational complexity especially to the model checking problem for which many tools developed in the area of decidability have proved to be useful for more than two decades it was conjectured in d seese the structure of the models of decidable monadic theories of graphs ann pure appl logic 53 1991 169 195 that decidability of monadic theories of countable structures implies that the theory can be reduced via interpretability to a theory of trees it is one of the main goals of this article to prove a variant of this conjecture for matroids representable over a finite field matroids can be viewed as a wide generalization of graphs and they seem to capture some second order properties in a more suitable way than graphs themselves cf the recent development in matroid structure theory j f geelen a h m gerards g p whittle branch width and well quasi ordering in matroids and graphs j combin theory ser b 84 2002 270 290 j f geelen a h m gerards n robertson g p whittle excluding a planar graph from a gf q representable matroid manuscript 2003 more exactly we prove for every finite field f that any class of f representable matroids with a decidable mso theory must have uniformly bounded branch width moreover we show that bounding the branch width of all matroids in general is not sufficient to obtain a decidable mso theory our paper gives a rather detailed introduction to these different subjects and shows that a blend of ideas and methods from logic together with structural matroid theory can lead to new tools and algorithms and can shed light on some old open problems

a one sided studentized range test for testing against a simple ordered alternative abstract consider the usual balanced one way fixed effects analysis of variance anova model x ij i e ij 1 j n 1 i k where the e ij are independent n 0 sgrave 2 random variables and i is the mean of the ith treatment 1 i k the i and sgrave 2 are unknown parameters let x i be the sample mean of the ith treatment based on n observations 1 i k and let s 2 be an unbiased estimate of sgrave 2 which is distributed independently of the x i as a 2 2 v v random variable usually the anova mean squared error with v k n 1 df is used as the estimate s 2 a problem that has received considerable attention is that of testing the null hypothesis h 0 1 k against the simple ordered alternative hypothesis h a 1 k with at least one strict inequality see e g barlow bartholomew bremner and brunk 1972 and robertson wright and dykstra 1988 various test procedures have been proposed for this problem such as the likelihood ratio test

the evaluation of first order substitution is monadic second order compatible we denote first order substitutions of finite and infinite terms by function symbols indexed by the sequences of first order variables to which substitutions are made we consider the evaluation mapping from infinite terms to infinite terms that evaluates these substitution operations this mapping may perform infinitely many nested substitutions so that a term which has the structure of an infinite string can be transformed into one isomorphic to an infinite binary tree we prove that this mapping is monadic second order compatible which means that a monadic second order formula expressing a property of the output term produced by the evaluation mapping can be translated into a monadic second order formula expressing this property over the input term this implies that deciding the monadic second order theory of the output term reduces to deciding that of the input term as an application we obtain another proof that the monadic second order properties of the algebraic trees which represent the behaviours of recursive applicative program schemes are decidable this proof extends to hyperalgebraic trees these infinite trees correspond to certain recursive program schemes with functional parameters of arbitrary high type

closure properties of locally finite ω languages locally finite omega languages were introduced by ressayre in journal of symbolic logic volume 53 no 4 p 1009 1026 they generalize omega languages accepted by finite automata or defined by monadic second order sentences we study here closure properties of the family loc omega of locally finite omega languages in particular we show that the class loc omega is neither closed under intersection nor under complementation giving an answer to a question of ressayre

fundamental study the modular decomposition of countable graphs definition and construction in monadic second order logic we consider the notion of modular decomposition for countable graphs the modular decomposition of a graph given with an enumeration of its set of vertices can be defined by formulas of monadic second order logic another result is the definition of a representation of modular decompositions by low degree relational structures such relational structures can also be defined in the considered graph by monadic second order formulas

towards a descriptive set theory for domain like structures this is a survey of results in descriptive set theory for domains and similar spaces with the emphasis on the algebraic domains we try to demonstrate that the subject is interesting in its own right and is closely related to some areas of theoretical computer science since the subject is still in its beginning we discuss in detail several open questions and possible future development we also mention some relevant facts of effective descriptive set theory

the monadic second order logic of graphs x linear orderings graphs are finite and handled as relational structures we give some answers to the following general questions 1 1 for which classes of graphs c is it possible to specify a linear ordering of the set of vertices of each graph of c by fixed monadic second order formulas 2 2 for which classes of graphs c does there exist an extension l of monadic second order logic such that a subclass l of c is recognizable if and only if it is the class of graphs in c that satisfy a formula of l in this paper recognizability is understood in an algebraic sense relative to a finite set of graph operations and basic graphs that generate all graphs of c 3 3 for which classes of graphs c is it possible to construct in every graph of the class and by fixed formulas of a suitable extension of monadic second order logic its hierarchichal structure i e a finite term written with the operations and basic graphs of 2 that defines the considered graph applications concern dependency graphs of partially commutative words partial k paths cographs and graphs the modular decomposition of which uses prime graphs of bounded size

dpda s in atomic normal form and applications to equivalence problems abstract in this paper we introduce a new normal form for dpda s the atomic normal form as an application using also the concept of address language due to gorn 19 20 we give alternate and more direct proofs of results of courcelle 3 4 relating recursion schemes and dpda s address languages enable us to encode trees even when they are not locally finite as a consequence the decidability of a new class of schemes corresponding to the stateless dpda s of 26 is obtained

equivalences and transformations of regular systems applications to recursive program schemes and grammars abstract this work presents a unified theory of recursive program schemes context free grammars grammars on arbitrary algebraic structures and in fact recursive definitions of all kind by means of regular systems the equivalences of regular systems associated with either all their solutions or their least solutions in all domains of appropriate type satisfying a set of algebraic laws expressed by equations are systematically investigated and characterized in some cases in terms of system transformations by folding unfolding and rewriting according to the equational algebraic laws grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union and the same questions are raised for them we also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system this theory applies to grammars of many kinds which generate trees graphs etc we formulate some classical transformations of context free grammars in terms of correct transformations which only use folding unfolding and algebraic laws and we immediately obtain their correctness

a hierarchy of deterministic context free ω languages twenty years ago klaus w wagner came up with a hierarchy of regular sets that actually bears his name it turned out to be exactly the wadge hierarchy of the sets of words recognized by deterministic finite automata we describe the wadge hierarchy of context free languages which stands as an extension of wagner s work from automata to pushdown automata

ambiguity in omega context free languages we extend the well known notions of ambiguity and of degrees of ambiguity of finitary context free languages to the case of omega context free languages cfl accepted by buchi or muller pushdown automata we show that these notions may be defined independently of the buchi or muller acceptance condition which is considered we investigate first properties of the subclasses of omega context free languages we get in that way giving many examples and studying topological properties of cfl of a given degree of ambiguity

the maximum familywise error rate of fisher s least significant difference test abstract in this article an investigation is made of the maximum familywise error rate mfwer of fisher s least significant difference lsd test for testing the equality of k population means in a one way layout an exact expression for the mfwer is derived see theorem 1 for all balanced models and for an unbalanced model with k 3 populations type i models a close upper bound for the mfwer is derived for all unbalanced models with four or more populations type ii models these expressions are used to illustrate that the mfwer may greatly exceed the nominal size of the lsd test in addition a simple modification of the lsd test is proposed to control the mfwer this modified procedure has mfwer equal to the nominal level for type i models and no greater than for type ii models theorem 2 and is therefore recommended as an improvement over the lsd test the key to the analysis is two theorems concerning the ranges of independent normal random variables which are contained in the append

theory of traces abstract the theory of traces originated by a mazurkiewicz in 1977 is an attempt to provide a mathematical description of the behavior of concurrent systems its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand one can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs or even in the theory of labeled partial orders this paper attempts to present a major portion of the theory of traces in a unified way however it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved although traditionally most of the development in the theory of traces follows the string language theoretic line we try to demonstrate to the reader that the graph theoretic point of view may be more appropriate the paper essentially consists of two parts the first one sections 1 through 4 is concerned with the basic theory of traces the second one section 5 presents applications of the theory of traces to the theory of the behavior of concurrent systems where the basic system model we have chosen is the condition event system introduced by c a petri

finite automata and ordinals abstract several definitions of automata on words indexed by ordinals have been proposed previously the first one was introduced by buchi to prove the decidability of the monadic second order theory of denumerable ordinals wojciechowski studied the properties of these automata independently of the length of the input the second definition proposed by choueka works only on words of length less than n in this paper we restrict the domain of wojciechowski automata to the domain of choueka s ones that is given n we keep only sequences for n 1 in the language defined by a wojciechowski automaton in order to prove the equivalence between choueka automata and wojciechowski automata then we obtain the closure under complementation of the class of wojciechowski s definable sets and finally we give an algorithm for determinizing wojciechowski automata

x automata on ω words abstract for any storage type x the languages accepted by x automata are investigated six accepting conditions including those introduced by landweber are compared for x automata the inclusions between the corresponding six families of languages are essentially the same as for finite state automata apart from unrestricted automata also real time and deterministic automata are considered the main tools for this investigation are 1 a characterization of the languages accepted by x automata in terms of inverse x transductions of finite state languages and 2 the existence of topological upper bounds on some of the families of accepted languages independent of the storage type x

computer science and the fine structure of borel sets i wadge defined a natural refinement of the borel hierarchy now called the wadge hierarchy wh the fundamental properties of wh follow from the results of kuratowski martin wadge and louveau we give a transparent restatement and proof of wadge s main theorem our method is new for it yields a wide and unexpected extension from borel sets of reals to a class of natural but non borel sets of infinite sequences wadge s theorem is quite ineffective and our generalization clearly worsens in this respect yet paradoxically our method is appropriate to effectivize this whole theory in the context discussed below ii wagner defined on buchi automata accepting words of length a hierarchy and proved for it an effective analog of wadge s results we extend wagner s results to more general kinds of automata counters push down automata and buchi automata reading transfinite words the notions and methods developed in i are quite useful for this extension and we start to use them in order to look for extensions of the fundamental effective determinacy results of buchi landweber rabin and of courcelle walukiewicz

borel hierarchy and omega context free languages we give in this paper additional answers to questions of lescow and thomas a decade of concurrency lecture notes in computer science vol 803 springer berlin 1994 pp 583 621 proving topological properties of omega context free languages cfl which extend those of o finkel theoret comput sci 262 1 2 2001 669 697 there exist some cfl which are non borel sets and one cannot decide whether an cfl is a borel set we give also an answer to a question of niwinski problem on powers posed in the proceedings of the workshop logics and recognizable sets 1990 and of simonnet automates et th orie descriptive ph d thesis universit paris 7 1992 about powers of finitary languages giving an example of a finitary context free language l such that l is not a borel set then we prove some recursive analogues to preceding properties in particular one cannot decide whether an cfl is an arithmetical set finally we extend some results to context free sets of infinite trees

combining the advantages of one sided and two sided test procedures for comparing several treatment effects abstract we consider the one way layout for comparing k treatment effects i 1 i k hayter earlier proposed a one sided studentized range test osrt for testing the null hypothesis h o 1 2 k against the simple ordered alternative ha 1 2 k with at least one strict inequality the osrt gives a set of simultaneous confidence intervals for all ordered pairwise differences j i i 0 but provides two sided finite confidence intervals if the sample averages are all far apart

a multiple comparison procedure for hypotheses with gatekeeping structure we develop gatekeeping procedures that focus on comparing multiple treatments with a control when there are multiple endpoints our procedures utilize estimated correlations among individual test statistics without parametric assumptions we make comparisons with other gatekeeping procedures with respect to properties of the trade off in statistical power between families of hypotheses we introduce a reward function to facilitate these comparisons we illustrate our methods by simulation and an analysis of data from a randomized multi armed clinical trial copyright 2013 oxford university press

a generalized tukey conjecture for multiple comparisons among mean vectors abstract in this article the tukey kramer procedure for multiple comparisons of pairwise differences of mean vectors in multivariate normal distributions is considered a multivariate version of the tukey kramer procedure is presented and a generalized tukey conjecture of the conservativeness of the simultaneous confidence intervals for all pairwise comparisons by this procedure is affirmatively proved in the case of three correlated mean vectors some properties of the multivariate tukey kramer procedure are also presented and simulation results for some selected parameters are given

pooling batches in drug stability study by using constant width simultaneous confidence bands one important study objective in drug stability studies is to estimate the shelf life of a drug a key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf life for the drug in this paper constant width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches with a particular view to establish the practical equivalence of different batches this approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal it is shown how constant width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models in particular it is shown that constant width simultaneous confidence bands have a better chance to establish the equivalence than and so are preferable to the hyperbola shaped simultaneous confidence bands considered j am stat assoc 2004 99 395 403

the monadic second order logic of graphs vii graphs as relational structures abstract relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied we define operations on structures that are compatible with monadic second order logic and that are powerful enough to represent context free graph and hypergraph grammars of various types namely the so called hyperedge replacement c ednce and separated handle rewriting grammars several results concerning monadic second order properties of the generated sets are obtained in a uniform way we also give a logical characterization of the equational sets of structures that generalizes the ones obtained by engelfriet and courcelle for hyperedge replacement and c ednce sets of graphs

the borel hierarchy is infinite in the class of regular sets of trees abstract for all the borel classes of finite order we construct weakly acceptable sets of infinite trees representing these classes

clique detection models in computational biochemistry and genomics abstract many important problems arising in computational biochemistry and genomics have been formulated in terms of underlying combinatorial optimization models in particular a number have been formulated as clique detection models the proposed article includes an introduction to the underlying biochemistry and genomic aspects of the problems as well as to the graph theoretic aspects of the solution approaches each subsequent section describes a particular type of problem gives an example to show how the graph model can be derived summarizes recent progress and discusses challenges associated with solving the associated graph theoretic models clique detection models include prescribing a a maximal clique b a maximum clique c a maximum weighted clique or d all maximal cliques in a graph the particular types of biochemistry and genomics problems that can be represented by a clique detection model include integration of genome mapping data nonoverlapping local alignments matching and comparing molecular structures and protein docking

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

enumerating all connected maximal common subgraphs in two graphs we represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem we have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs these algorithms are based on variants of the bron kerbosch algorithm in this paper we explain the transformation of the maximal common subgraph problem into the clique problem we give a short summary of the variants of the bron kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs after introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs the results show the drastical reduction of the runtimes for the new algorithms

exact simultaneous confidence intervals for multiple comparisons among three or four mean values abstract a procedure for constructing exact simultaneous confidence intervals for a finite set of multiple comparisons among three or four groups is presented these confidence intervals are hyperbolic and based on an unbiased estimator of the mean values having a normal distribution with covariance matrix 2v where v is an arbitrary known positive definite matrix this procedure is used to study the amount of conservativeness of tukey kramer intervals for pairwise comparisons in an unbalanced one way analysis of variance design

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

a proof of the conjecture that the tukey kramer multiple comparisons procedure is conservative in this paper we present a first general proof of tukey s 1953 conjecture concerning the extension of the tukey multiple comparisons procedure to the case of unequal sample sizes thereby proving that the so called tukey kramer procedure is conservative in all cases also a brief history of the conjecture is given and some extensions and further problems concerning the procedure are discussed

pushdown automata with bounded nondeterminism and bounded ambiguity abstract measures for the amount of ambiguity and nondeterminism in pushdown automata pda are introduced for every finite k pdas with ambiguity at most k are shown to accept exactly the class of languages generated by context free grammars with ambiguity at most k pdas with an amount of nondeterminism at most k accept exactly the class of the unions of k deterministic context free languages for all finite or infinite k k with k k there is a language that can be accepted by a pda with ambiguity k and nondeterminism k but by no pda with less ambiguity or less nondeterminism for every finite k it is shown that the tradeoff from a description by a pda with ambiguity k 1 and nondeterminism k 1 to pdas with ambiguity k is bounded by no recursive function the tradeoff from pdas with ambiguity 1 and nondeterminism k 1 to pdas with nondeterminism k also is bounded by no recursive function the tradeoff from pdas with branching k to pdas with ambiguity k and branching k is at most exponential

the monadic second order logic of graphs xii planar graphs and planar maps we prove that we can specify by formulas of monadic second order logic the unique planar embedding of a 3 connected planar graph if the planar graph is not 3 connected but given with a linear order of its set of edges we can also define a planar embedding by monadic second order formulas we cannot do so in general without the ordering even for 2 connected planar graphs the planar embedding of a graph can be specified by a relational structure called a map which is a graph enriched with a circular ordering of the edges incident with each vertex this circular ordering called a rotation system represents a planar embedding of the neighbourhood of each vertex for each connected map one can define a linear order on its vertices by formulas of monadic second order logic hence we have for planar graphs some kind of equivalence between linear orderings and planar embeddings

inclusion exclusion bonferroni identities and inequalities for discrete tube like problems via euler characteristics identity for the union of finitely many balls in d dimensional euclidean space with a single correction term this result also holds in the d dimensional sphere these results form the basis for a discrete theory of tubes which up to now has been continuous in nature the spherical result is used to give a simulation method for finding critical probabilities for multiple comparisons procedures and a computer program implementing the method is described numerical results are presented which demonstrate that in the tails of the distribution probability estimates based on the method tend to exhibit less variability than estimates based on naive simulation 1 introduction this paper touches on several areas of mathematics statistics and elementary probability theory the main results are somewhat technical in proof but easily stated consider a finite collection of measurable subsets ai n the classical inclusion exclusion identity is n

the efficiency of simulation based multiple comparisons a frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of or equivalent to a univariate linear model this problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal in other cases conservative solutions can be obtained by the methods of scheffe bonferroni or sidak 1967 journal of the american statistical association 62 626 633 here we investigate the efficiency of using a simulated critical point for exact intervals which has been suggested before but never put to serious test we find the simulation based method to be completely reliable and essentially exact sample size savings are substantial in our settings 3 19 over the sidak method 4 37 over the bonferroni method and 27 33 over the scheffe method we illustrate the efficiency and flexibility of the simulation based method with case studies in physiology and marine ecology

exact confidence bands for linear regression over intervals abstract exact simultaneous confidence intervals and bands for the regression line on a set cx in simple linear regression have been known only when cx is a finite set with one or two points or when cx is a finite or infinite interval otherwise conservative bands have been used in this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points also tables are provided for cases of finite cx with three points and of cx an interval

topological properties of omega context free languages abstract this paper is a study of topological properties of omega context free languages cfl we first extend some decidability results for the deterministic ones dcfl proving that one can decide whether an dcfl is in a given borel class or in the wadge class of a given regular language we prove that cfl exhaust the hierarchy of borel sets of finite rank and that one cannot decide the borel class of an cfl giving an answer to a question of lescow and thomas a decade of concurrency springer lecture notes in computer science vol 803 springer berlin 1994 pp 583 621 we give also a partial answer to a question of simmonet automates et theorie descriptive ph d thesis universite paris 7 march 1992 about omega powers of finitary languages we show that buchi landweber s theorem cannot be extended to even closed cfl in a gale stewart game with a closed cfl winning set one cannot decide which player has a winning strategy from the proof of topological properties we derive some arithmetical properties of cfl

refined pivot selection for maximal clique enumeration in graphs this article re examines the pivoting bron kerbosch algorithm for identifying all maximal cliques within a graph a curious result is presented there exist pivot candidates which may be selected with no penalty to the worst case running time even if these vertices do not satisfy the established conditions for the known complexity bound hence such pivots may be selected eagerly a refined pivot selection process is described and the preservation of the established worst case bound is proved additionally empirical evidence shows that the revised algorithm is notably faster than bron kerbosch with tomita style pivot selection

monadic second order logic on tree like structures an operation m which constructs from a given structure m a tree like structure whose domain consists of the finite sequences of elements of m is considered a notion of automata running on such tree like structures is defined it is shown that automata of this kind characterise expressive power of monadic second order logic msol over tree like structures using this characterisation it is proved that msol theory of a tree like structure is effectively reducible to that of the original structure as another application of the characterisation it is shown that msol on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator

multiple comparison methods for means multiple comparison methods mcms are used to investigate differences between pairs of population means or more generally between subsets of population means using sample data although several such methods are commonly available in statistical software packages users may be poorly informed about the appropriate method s to use and or the correct way to interpret the results this paper classifies the mcms and presents the important methods for each class both simulated and real data are used to compare methods and emphasis is placed on correct application and interpretation we include suggestions for choosing the best method mathematica programs developed by the authors are used to compare mcms by taking advantage of mathematica s notebook structure an interested student can use these programs to explore the subject more deeply the programs and examples used in the article are available at http www cs gasou edu faculty rafter mcmm