Existing methods for alias analysis of recursive pointer data structures are based on two approximation techniques: k-limiting, which blurs distinction between sub-objects below depth k; and store-based (or equivalently location or regionbased) approximations, which blur distinction between elements of recursive data structures. Although notable progress in interprocedural alias analysis has been recently accomplished, very little progress in the precision of analysis of recursive pointer data structures has been seen since the inception of these approximation techniques by Jones and Muchnick a decade ago. As a result, optimizing, verifying and parallelizing programs with pointers has remained difficult. We present a new parametric framework for analyzing recursive pointer data structures which can express a new natural class of alias information not accessib...

this paper. 2 Background 2.1 Outline of the commutative theory Here is a brief review of the classical theory of symmetric functions. A standard reference is Macdonald's book [Mcd]. The notations used here are those of [LS1]. Denote by X = fx 1 ; x 2 ; : : : g an infinite set of commutative indeterminates, which will be called a (commutative) alphabet. The elementary symmetric functions k (X) are then defined by means of the generating series (X; t) := k (X) = (1 + x i t) : (1) The complete homogeneous symmetric functions S k (X) are defined by oe(X; t) := S k (X) = (1 \Gamma x i t) ; (2) so that the following fundamental relation holds oe(X; t) = (X; \Gammat) : (3) The power sums symmetric functions / k (X) are defined by /(X; t) := / k (X) = x i (1 \Gamma x i t) : (4) These generating series satisfy the following relations /(X; t) = log oe(X; t) = \Gamma log (X; \Gammat) ; (5) d dt oe(X; t) = oe(X; t) /(X; t) ; (6) dt (X; \Gammat) = /(X; t) (X; \Gammat) : (7) Formula (7) is known as Newton's formula. The so-called fundamental theorem of the theory of symmetric functions states that the k (X) are algebraically independent. Therefore, any formal power series f(t) = 1 + k1 a k t may be considered as the specialization of the series (X; t) to a virtual set of arguments A. The other families of symmetric functions associated to f(t) are then defined by relations (3) and (5). This point of view was introduced by Littlewood and extensively developped in [Li1]. For example, the specialization S n = 1=n! transforms the generating series oe(X; t) into the exponential function e . Thus, considering oe(X; t) as a symmetric analog of e , one can construct symmetric analogs for several related functions, such as trigonometric func...

We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. For a subclass including all safe Free Choice Petri nets, we obtain reduced heap realizations using structural properties of the net (covering by safe state machine components). We illustrate the heap-based modeling by the typical case of safe jobshops. For a periodic schedule, we obtain a heap-based throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is interested in the successive evaluation of a large number of possible schedules. Keywords Timed Petri nets, automata with multiplicities, heaps of pieces, (max,+) semiring, scheduling. I. Introduction The purpose of this paper 1 is to prove the following result: Timed safe Pe...

When a discrete-event system P consists of several subsystems P1,..., Pn that oper-ate concurrently, a natural approach to the supervisory control problem is to synthesize a ’local ’ controller Si for each subsystem Pi and operate the individually controlled sub-systems Si/Pi concurrently. Such an approach is called concurrent supervisory control and is closely related to decentralized supervisory control as studied in [4] and [5]. In the present paper simple and easily computable conditions are developed, that guarantee when concurrent supervisory control can achieve the optimal behavior achievable by a global supervisor. To achieve the optimal behavior, two specific concurrent control strategies are introduced. Key words: discrete event systems, supervisory control, concurrency, decentralization, separability. 1

We present several identities involving quasi-minors of noncommutative generic matrices. These identities are specialized to quantum matrices, yielding q-analogues of various classical determinantal formulas.

Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speech-to-text processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted first-order logic and show that aperiodic series coincide with the first-order definable ones, if the semiring is locally finite, commutative and has some aperiodicity property. 1

A fundamental problem for imitation is to create an appropriate (partial) mapping between the body of the system being imitated and the imitator. By considering for each of these two systems an associated automata (resp. transformation semigroup) structure, attempts at such mapping can be considered relational homomorphisms. This paper shows how mathematical techniques can then be applied to characterize how far such a relation is from a successful imitation. For the imitator and the imitated, affordances in the agent-environment structural coupling are likely to be different, all the more in the case of dissimilar embodiment. We argue that the use of what is afforded to the imitator to attain corresponding effects or, as in dance, sequences of effects, is necessary and sufficient for successful imitation. Moreover, the judged degree of success or failure of an imitation depends on some externally imposed or --- in the case of automonous agents --- internally determined criteria on eff...

We investigate bottom-up and top-down deterministic automata on unranked trees. We show that for an appropriate definition of bottom-up deterministic automata it is possible to minimize the number of states e#ciently and to obtain a unique canonical representative of the accepted tree language. For top-down deterministic automata it is well known that they are less expressive than the non-deterministic ones.

The sh-verification tool comprises computing abstractions of finite-state behaviour representations as well as automata and temporal logic based verification approaches. To be suitable for the verification of so called co-operating systems, a modified type of satisfaction relation (approximate satisfaction) is considered. Regarding abstraction, alphabetic language homomorphisms are used to compute abstract behaviours. Toavoid loss of important information when moving to the abstract level, abstracting homomorphismshave to satisfy a certain property called simplicity on the concrete (i.e. not abstracted) behaviour. The well known state space explosion problem is tackled by a compositional method combined with a partial order method.

this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.