Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets or pomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. Th...

this paper was developed by Murray Shanahan (building upon earlier work by Kowalski and Sergot [64]) in a series of papers [102], [101], [103] and [100]. Shanahan's discussion of the frame problem and his proposed solution can also be found in the book [104]

this paper [Pavise 1982]. In order to simplify the present discussion we shall adopt the Gregorian calendar as our prototypical calendar. Calendar years are typically an integral number of days, yet there are not (currently) an integral number of days in any astronomically computed year. For example, for the Gregorian calendar year 1985, the anomalistic year was 365:259; 641 ephemeris days, the tropical year was in the northern hemisphere's Spring and fast in its Fall; and unpredictable variations, probably caused by differing rates of rotation between the core and the mantle. The gradual slowing of the rate of rotation adds about 1.5 milliseconds to the length of a day (in comparison to other clocks) during a century. The length of a day could fluctuate by 4 milliseconds over the course of a decade due to the unpredictable variations. Finally, seasonal variations can cause changes on the order of 1.2 milliseconds in the length of a day during a year [Howse 1980]. Another factor to consider in making precise sidereal time measurements is polar wander . Polar wander is a slight circular wobble of the Earth around the North/South pole on the order of 8 meters a year. Polar wander shifts an observer's meridian by a fraction each day (recall that the observer's meridian is used to determine when the sidereal and solar days start). The size of the shift depends on the observer's latitude. The family of universal times attempts to correct for these variations. UT0 is the mean solar time for the prime meridian computed by direct astronomical observations. The prime meridian is the 0

Programming language research should be driven by the needs of specific application domains, such as real-time embedded systems, multimedia, distributed data-base management applications, etc. For instance, most often large real-time applications involve distributed and concurrently but asynchronously operating devices. The correctness of the integrated systems depends not only on the correct operation of each individual device, but also on the correct coordination among these devices. Furthermore, the correctness of device operation and cooperation requires that both the underlying logical computation be correct and the computation satisfy some notion of quantitative timing requirements. This thesis is a case study for how a language should be designed to suit a specific application domain. Specifically, I have designed RTsynchronizers (Real Time Synchronizers), a high-level programming language abstraction for specifying real-time coordination constraints between objects in a distrib...

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized for giving a new geometric and physical interpretation of more general convolution integrals of the Volterra type. Besides this, a new physical interpretation is suggested for the Stieltjes integral.

this paper, section 3, is devoted to a fairly detailed exposition of Prior's basic tense logic; the aim of this is not only to introduce the readers to this particular system, but perhaps even more to acquaint them with the kind of questions that temporal logicians tend to ask. In the sections 4 and 5 we present some extensions and alternatives to this base system. In section 6 we sketch some developments that have taken place over the last ten years or so. Finally, in the epilogue we try to answer the question what Temporal Logic is; this section also contains a short list of monographs surveying the field of temporal logic. 2 Flows of time

We address the problem of timing constraint derivation and validation for reactive and real-time embedded systems. We assume that such a system is structured into its tasks, and the structure is modeled using a task graph. Our solution uses the timing behavior committed by the environment to the system first to derive the timing constraints on the system's internal behavior and then use them to derive and validate the timing constraints on the system's external behavior. Our solution consists of the following contributions: (1) a generalized task graph model and a comprehensive classification of timing constraints, (2) algorithms for derivation and validation of timing constraints of the system modeled in the generalized task graph model, (3) new and improved algorithms for finding the performance of cyclic embedded systems and a comprehensive comparison of the existing algorithms, (4) a general formulation of the problem of debugging timing violations in cyclic embedded systems and it...

this article Walker wants to show that the instants obtained from the partially ordered set form a complete linear order (that is, the temporal experience of an observer in physics). He defined the relation of overlap in function of the precedence relation, i.e if two events a and b are such that a < b and b < a are false, then we say that a# b, and give two axioms for those relations, (i) an event always overlaps itself, (ii) axiom A6 of Russell's construction. The real new step in the construction is to define an instant as cut of the set of events in three parts, (P, C, F ), which corresponds to a partition of the set into "past", "current" and "future"

Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators with-out requiring or referring to a fictitious external observer is addressed, and this in turn rephrases and removes the traditional Measurement Problem inherent in the Copenhagen interpretation of quantum mechanics. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically,

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