event structures and trace monoids event structures are a poset based model for describing the behaviour of distributed systems they give rise to a well understood class of scott domains event structures are also related to petri nets in a fundamental way trace monoids are a string based formalism for describing the behaviour of distributed systems they have an independent theory rooted in the theory of formal languages here we obtain a representation of trace monoids in terms of a subclass of labelled event structures

the poset of infinitary traces gastin p and b rozoy the poset of infinitary traces theoretical computer science 120 1993 101 121 partially commutative monoids also called trace monoids are among the most studied formalisms to describe the behaviour of distributed systems in order to model systems which never stop we have to consider an extension of traces namely infinite traces finite trace monoids are strongly related to partial order sets posets domains and went structures which are other models to describe the behaviour of distributed systems the aim of this paper is to establish similar connexions between infinite trace monoids posets and event structures we prove that the set of finite and infinite traces with the prefix order is a scott domain and a coherently complete prime algebraic poset moreover we establish a representation theorem between the class of jirtite and infinite trace posets and a subclass of labelled prime event structures

efficient solution of some problems in free partially commutative monoids abstract linear time algorithms are presented for several problems concerning words in a partially commutative monoid including whether one word is a factor of another and whether two words are conjugate in the monoid

on the dynamic finger conjecture for splay trees part ii the proof the following result is shown on an n node splay tree the amortized cost of an access at distance d from the preceding access is o log d 1 in addition there is an o n initialization cost the accesses include searches insertions and deletions

distributionally robust optimization under moment uncertainty with application to data driven problems stochastic programming can effectively describe many decision making problems in uncertain environments unfortunately such programs are often computationally demanding to solve in addition their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters in this paper we propose a model that describes uncertainty in both the distribution form discrete gaussian exponential etc and moments mean and covariance matrix we demonstrate that for a wide range of cost functions the associated distributionally robust or min max stochastic program can be solved efficiently furthermore by deriving a new confidence region for the mean and the covariance matrix of a random vector we provide probabilistic arguments for using our model in problems that rely heavily on historical data these arguments are confirmed in a practical example of portfolio selection where our framework leads to better performing policies on the true distribution underlying the daily returns of financial assets

representation of computations in concurrent automata by dependence orders abstract an automaton with concurrency relations a is a labelled transition system with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each other the concurrency relations induce a natural equivalence relation for finite computation sequences we investigate two graph theoretic representations of the equivalence classes of computation sequences and obtain that under suitable assumptions on a they are isomorphic furthermore the graphs are shown to carry a monoid operation reflecting precisely the composition of computations this generalizes fundamental graph theoretical representation results due to mazurkiewicz in trace theory

stochastic programming approach to optimization under uncertainty in this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems we argue that two stage say linear stochastic programming problems can be solved with a reasonable accuracy by monte carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages we discuss an extension of coherent risk measures to a multistage setting and in particular dynamic programming equations for such problems

star free trace languages abstract generalizing a classical result of schutzenberger to free partially commutative monoids we prove that the family of star free trace languages coincides with the family of aperiodic trace languages

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

an extension of kleene s and ochman ski s theorems to infinite traces abstract as was noted by mazurkiewicz traces constitute a convenient tool for describing finite behaviour of concurrent systems extending in a natural way mazurkiewicz s original definition infinite traces have recently been introduced enabling one to deal with infinite behaviour of nonterminating concurrent systems in this paper we examine the basic families of recognizable sets and of rational sets of infinite traces the seminal kleene characterization of recognizable subsets of the free monoid and its subsequent extensions to infinite words due to buchi and to finite traces due to ochmanski are the cornerstones of the corresponding theories the main result of our paper is an extension of these characterizations to the domain of infinite traces using recognizing and weakly recognizing morphisms as well as a generalization of the schutzenberger product of monoids we prove various closure properties of recognizable trace languages moreover we establish normal form representations for recognizable and rational sets of infinite traces

dynamic optimality almost we present an o lg lg n competitive online binary search tree improving upon the best previous trivial competitive ratio of o lg n this is the first major progress on sleator and tarjan s dynamic optimality conjecture of 1985 that o 1 competitive binary search trees exist

maximal serializability of iterated transactions abstract the serializability condition is usually considered in order to maintain the consistency of a database in the presence of conflicting accesses to the database performed by concurrent transactions this serializability condition is considered herein as a general synchronization problem among transactions or processes which can be iterated infinitely often the behaviour of such a system of transactions is represented by an infinite word over the alphabet of the operations performed by the transactions then a characterization of the prefixes of such behaviours is given and it is shown that satisfying the serializability condition so called correct behaviours is given and it is shown that the set of all correct behaviours can be controlled by a finite automaton as an example the classical dining philosophers problem is shown to be entirely modelled and solved as a serializability problem

recognizable subsets of some partially abelian monoids we show that in a free partially abelian monoid generated by a finite alphabet a the subset x of a containing all the words equivalent to a product of words of x is rational if x is a finite set of words each word containing at least one occurrence of any letter of a we suppose that the graph the vertices of which are letters of a and the edges of which correspond to noncommuting pairs of letters is connected

lower bounds for accessing binary search trees with rotations two methods are given for obtaining lower bounds on the cost of accessing a sequence of nodes in a symmetrically ordered binary search tree in a model where rotations can be done on the tree and the entire sequence is known before accessing begins but the accesses must be done in the order given for example it can be proven that the bit reversal permutation requires theta n log n time to access in this model it is also shown that the expected cost of accessing random sequences in this model is the same as it is for the case where the tree is static

stochastic optimization problems with incomplete information on distribution functions the main purpose of this paper is to discuss numerical optimization procedures based on duality theory for stochastic extremal problems in which the distribution function is only partially known we formulate such problems as minimax problems in which the inner problem involves optimization with respect to probability measures the latter problem is solved using generalized linear programming techniques then we state the dual problem to the initial stochastic optimization problem numerical procedures that avoid the difficulties associated with solving the inner problem are proposed

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

a study on splay trees abstract we study the dynamic optimality conjecture which predicts that splay trees are a form of universally efficient binary search tree for any access sequence we reduce this claim to a regular access bound which seems plausible and might be easier to prove this approach may be useful to establish dynamic optimality

on regular trace languages abstract we characterize here the free partially commutative monoids the regular sets of which form a boolean algebra or are all unambiguous these are in both cases the free products of free commutative monoids this result has been established independently by other authors but the method used here is original it is based on the properties of generalized automata on free products of monoids

applying the minimax criterion in stochastic recourse programs we consider an optimization problem in which some uncertain parameters are replaced by random variables the minimax approach to stochastic programming concerns the problem of minimizing the worst expected value of the objective function with respect to the set of probability measures that are consistent with the available information on the random data only very few practicable solution procedures have been proposed for this problem and the existing ones rely on simplifying assumptions in this paper we establish a number of stability results for the minimax stochastic program justifying in particular the approach of restricting attention to probability measures with support in some known finite set following this approach we elaborate solution procedures for the minimax problem in the setting of two stage stochastic recourse models considering the linear recourse case as well as the integer recourse case since the solution procedures are modifications of well known algorithms their efficacy is immediate from the computational testing of these procedures and we do not report results of any computational experiments

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

recognizable languages in concurrency monoids automata with concurrency relations a are labelled transition systems with a collection of binary relations indicating when two actions in a given state of the automaton are concurrent we investigate concurrency monoids m a comprising all finite computation sequences of a modulo a canonical congruence induced by the concurrency relations with composition as monoid operation under suitable assumptions on a we obtain a kleene type characterization of the recognizable languages of m a this generalizes results of cori metivier perrin and ochmanski in trace theory

local testability from words to traces a suitable definition the family of locally testable languages has been extensively studied we propose an extension of the notion of local testability from the free monoid to the free partially commutative monoid the so called trace monoid we show that to formalize the notion of locality in traces is conceptually difficult and we introduce a new kind of factor which takes into account these difficulties thus we define a locally testable trace language as a union of classes of a new equivalence relation of a finite index which is proved to be a congruence using some combinatorics on traces then we give a set theoretic characterization of the family of locally testable trace languages in terms of some sets called here quasi ideals as a generalization of ideals in words finally analyzing the extreme cases of the free monoid and the free commutative monoid we prove that this new family becomes exactly that of locally testables languages in the case of words

the shuffle algebra and its derivations abstract the shuffle algebra on a partially commutative alphabet and its derivations are studied the derivation of the shuffle algebra is characterized in terms of admissible mappings the module of all derivations of the shuffle algebra is proved to be isomorphic to the free partially commutative power series lie algebra with the coefficient ring extended the orthogonality between the lie elements and the proper shuffles is established

sample average approximation method for compound stochastic optimization problems the paper studies stochastic optimization programming problems with compound functions containing expectations and extreme values of other random functions as arguments compound functions arise in various applications a typical example is a variance function of nonlinear outcomes other examples include stochastic minimax problems econometric models with latent variables and multilevel and multicriteria stochastic optimization problems as a solution technique a sample average approximation saa method also known as statistical or empirical sample mean method is used the method consists in approximation of all expectation functions by their empirical means and solving the resulting approximate deterministic optimization problems in stochastic optimization this method is widely used for optimization of standard expectation functions under constraints in this paper saa method is extended to general compound stochastic optimization problems the conditions for convergence in mean almost sure

asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems we study the asymptotic behavior of the statistical estimators that maximize a not necessarily dieren tiable criterion function possibly subject to side constraints equalities and inequalities the consistency results generalize those of wald and huber conditions are also given under which one is still able to obtain asymptotic normality the analysis brings to the fore the relationship between the problem of nding statistical estimators and that of nding the optimal solutions of stochastic optimization problems with partial information the last section is devoted to the properties of the saddle points of the associated lagrangians

extreme points of sets of randomized strategies in constrained optimization and control problems this paper concerns the existence and characterization of optimal randomized strategies for some constrained optimization and control problems we first present a characterization of the extreme points of a set of randomized strategies that satisfy n moment like constraints conditions are given under which those extreme points are randomizations of at most n 1 deterministic strategies this result is then applied to obtain the existence and characterization of optimal strategies for a class of deterministic allocation like optimization problems and their young relaxations similar results are obtained for constrained markov control processes in borel spaces

process flexibility a distribution free bound on the performance of k chain process flexibility has been widely applied in many industries as a competitive strategy to improve responsiveness to demand uncertainty an important flexibility concept is the long chain proposed by jordan and graves 1995 jordan wc graves sc 1995 principles on the benefits of manufacturing process flexibility management sci 41 4 577 594 the effectiveness of the long chain has been investigated via numerical as well as theoretical analysis for specific probability distributions of the random demand in this paper we obtain in closed form a distribution free bound on the ratio of the expected sales of the long chain relative to that of full flexibility our bound depends only on the mean and standard deviation of the random demand but compares very well with the ratio that uses complete information of the demand distribution this suggests the robustness of the performance of the long chain under different distributions we also prove a similar result for k chain a more general flexibility

mo bius functions and confluent semi commutations abstract dickert 1988 settled a well known conjecture on unambiguous liftings to words of mobius functions for free partially commutative monoids he established thereby a new bridge from the theory of formal power series to the theory of complete semi thue systems as an open question it was asked whether this approach has a generalization to a relative situation where we do not lift to the free word case but only to some level of less commutation this question has been reconsidered by konig 1992 and a conjecture has been formulated there our results solve the open problem and settle this conjecture remark 4 8 we show that there is a canonical one to one correspondence between unambiguous mobius functions and confluent semi commutation systems theorem 5 1 this identification is due to some graph theoretic characterizationobtained by diekert 1991 and which allows one to apply some interesting complexity results section 6 our results can be viewed as a contribution to the combinatorial theory of mobius functions and to the theory of rewriting on traces

synchronization expressions with extended join operation synchronization expressions are high level constructs used for specifying minimal synchronization constraints of parallel processes their semantics is defined by the corresponding synchronization language the original definition of synchronization expressions 12 13 forces the languages to be closed under rewriting rules that for instance do not preserve regularity here we propose an extension of the syntactic definition of synchronization expressions and an appropriate modification of their semantics the extended definition has the advantage that it allows us to eliminate the less well motivated transformations rewriting rules describing properties of synchronization languages we show that the modified rewriting rules preserve regularity of the languages also we obtain a characterization of finite synchronization languages as the family consisting of languages satisfying the start termination property and closed under three types of simple rewriting rules

a trace semantics for petri nets a generalization of the notion of trace is proposed this enables us to associate with each petri net a single behavioural object namely a poset of generalized traces a characterization is given of the trace languages defined by petri nets we show that the general event structures of winskel and the stable event structures can also be characterized in terms of our trace languages one consequence is that in this framework stable event structures general event structures and petri nets constitute a strictly ascending chain in terms of expressive power

on a class of minimax stochastic programs for a particular class of minimax stochastic programming models we show that the problem can be equivalently reformulated into a standard stochastic programming problem this permits the direct use of standard decomposition and sampling methods developed for stochastic programming we also show that this class of minimax stochastic programs is closely related to a large family of mean risk stochastic programs where risk is measured in terms of deviations from a quantile

the word problem for 1lc congruences is np hard in this paper it is proved that the word problem for congruences generated by subsets of abc acb a a e b c a is np hard these congruences are a generalization of mazurkiewicz s traces

asynchronous automata versus asynchronous cellular automata in this paper we compare and study some properties of two mathematical models of concurrent systems asynchronous automata zielonka 1987 and asynchronous cellular automata zielonka 1989 first we show that these models are polynomially related exhibiting polynomial time reductions between them subsequently we prove that in spite of that the classes of asynchronous automata and of asynchronous cellular automata recognizing a given trace language are in general deeply different in fact we exhibit a recognizable trace language t with the following properties there exists a unique minimum asynchronous automaton accepting t does not exist a unique minimum asynchronous cellular automaton but there are infinitely many minimal i e unreducible nonisomorphic asynchronous cellular automata accepting t we characterize the class of concurrent alphabets for which every recognizable trace language admits a minimum finite state asynchronous cellular automaton as the class of alphabets with full concurrency relation finally extending a result of bruschi et al 1988 we show that for every concurrent alphabet with nontransitive dependency relation there exists a trace language accepted by infinitely many minimal nonisomorphic asynchronous automata

on the sequential access theorem and deque conjecture for splay trees we give a new simple proof for the sequential access theorem for splay trees for an n node splay tree our bound on the number of rotations is 4 5n with a smaller constant than the bound of 10 8n concluded by tarjan we extend our proof to prove the deque conjecture for output restricted deques our proofs provide additional insights into the workings of splay trees

price of correlations in stochastic optimization when decisions are made in the presence of high dimensional stochastic data handling joint distribution of correlated random variables can present a formidable task both in terms of sampling and estimation as well as algorithmic complexity a common heuristic is to estimate only marginal distributions and substitute joint distribution by independent product distribution in this paper we study possible loss incurred on ignoring correlations through a distributionally robust stochastic programming model and we quantify that loss as price of correlations poc using techniques of cost sharing from game theory we identify a wide class of problems for which poc has a small upper bound to our interest this class will include many stochastic convex programs uncapacitated facility location steiner tree and submodular functions suggesting that the intuitive approach of assuming independent distribution acceptably approximates the robust model for these stochastic optimization problems additionally we demonstrate hardness of bounding poc via examples of subadditive and supermodular functions that have large poc we find that our results are also useful for solving many deterministic optimization problems like welfare maximization k dimensional matching and transportation problems under certain conditions

a compromise solution for the multiobjective stochastic linear programming under partial uncertainty abstract this paper solves the multiobjective stochastic linear program with partially known probability we address the case where the probability distribution is defined by crisp inequalities we propose a chance constrained approach and a compromise programming approach to transform the multiobjective stochastic linear program with linear partial information on probability distribution into its equivalent uniobjective problem the resulting program is then solved using the modified l shaped method we illustrate our results by an example

partial commutations and faithful rational transductions abstract we study the operation of partial commutation in connection with other operations such as partitioned commutation twin shuffle intersection and faithful rational transductions from that study we get a very simple characterization for the following families of languages multi reset bnp and q the family of quasirealtime languages

membership problems for regular and context free trace languages abstract trace languages have been introduced in order to describe the behaviour of concurrent systems in the same way as usual formal languages do for sequential system they can be defined as subsets of a free partially commutative monoid and a theory of trace languages can be developed generalizing the usual formal languages theory in this paper the time complexity of membership problems for regular and context free trace languages is investigated it is proved that the membership problem for context free trace languages can be solved in time o bm n where is the dimension of the greatest clique of the concurrency relation c and bm n is the time required for multiplying two arbitrary n n boolean matrices for regular trace languages our method gives an algorithm which requires o n time finally the uniform membership problem is shown to be np complete

guaranteed bounds for general nondiscrete multistage risk averse stochastic optimization programs in general multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty such infinite problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies in this paper we demonstrate how one can find guaranteed bounds i e finite tree models for which the optimal values give upper and lower bounds for the optimal value of the original infinite problem typically there is a gap between the two bounds however this gap can be made arbitrarily small by making the approximating trees bushier we consider approximations in the first order stochastic sense in the convex order sense and based on subgradient approximations their use is shown in a multistage risk averse production problem

the kleene schutzenberger theorem for formal power series in partially commuting variables kleene s theorem on the coincidence of regular and rational languages in free monoids has been generalized by schutzenberger to a description of the recognizable formal power series in noncommuting variables over arbitrary semirings and by ochmanski to a characterization of the recognizable languages in trace monoids we will describe the recognizable formal power series over arbitrary semirings and in partially commuting variables i e over trace monoids we prove that the recognizable series are certain rational power series which can be constructed from the polynomials by using the operations sum product and a restricted star which is applied only to series for which the elements in the support all have the same connected alphabet the converse is true if the underlying semiring is commutative moreover if in addition the semiring is idempotent then the same result holds with a star restricted to series for which the elements in the support have connected possibly different alphabets it is shown that these assumptions over the semiring are necessary this provides a joint generalization of kleene s schutzenberger s and ochmanski s theorems

probabilistic estimation of the number of prefixes of a trace abstract we present a generating function technique to evaluate the number of strings of a given length recognized by a particular kind of finite state automaton using the method we determine some asymptotic estimations of the number of prefixes in free partially commutative monoids more precisely we prove that for every concurrent alphabet c assuming equiprobable strings all of length n the average number of prefixes of a trace of length n is n k o n k 1 and its variance is o n 2 k 1 where k is the number of components of the dependency graph c c and is a rational constant depending only on c these combinatorial results allow to determine the probabilistic behaviour of some algorithms for problems on trace languages including the membership problems for regular and context free trace languages

a measure approximation for distributionally robust pde constrained optimization problems in numerous applications scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system this data is then used to inform decisions such as controls and designs consequently it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs in this paper we consider optimal control and design problems constrained by partial differential equations with uncertain inputs we do not assume a known probabilistic model for the inputs but rather we formulate the problem as a distributionally robust optimization problem where the outer minimization problem determines the control or design while the inner maximization problem determines the worst case probability measure that matches desired characteristics of the data we analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique bas