E. Harel. Temporal analysis of real-time systems. Master's thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....use the variable now) as the current time. We refer to this approach as the explicit clock approach, because the only new element is the ability to refer explicitly to the clock. Scattered examples of this method of expressing timing properties have been presented in [PdR82] in [Ron84] and in [Har88, PH88] A more systematic exposition of this approach and its applications can be found in [Ost90] where the explicit clock language is called Real time Temporal Logic, and in [LA92] Explicit clock temporal logics have been analyzed for their complexity and expressiveness in [AH90] and in ....

E. Harel. Temporal analysis of real-time systems. Master's thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.

.... specification of timing properties has been advocated by Koymans, Vytopil, and de Roever [KVdR83, KdR85, Koy90] although an early proposal by Bernstein and Harter can be viewed as a precursor [BH81] More applications of the boundedoperator method for expressing timing constraints can be found in [SPE84, Har88, PH88, HW89, Lew90]. Bounded operators have been analyzed for their expressiveness and complexity in [EMSS89, ACD90, AH90, AFH91] To be concrete, let us define a propositional linear time logic that employs time bounded temporal operators. The formulas of this bounded operator logic are built from atomic ....

....specified by the formula 8x: 2( p T = x) 3(q T x 3) Here, the global variable x is bound to the time of every state in which p is observed. We refer to the use of a clock variable as the explicit clock notation. Examples of this method for expressing timing constraints can be found in [PdR82, Ron84, Har88, PH88, Ost90, LA]; it has been studied for its expressiveness and complexity in [AH90, HLP90] Let us once again define a propositional linear time logic with an interval based strictly monotonic real time semantics. As before, let V be a set of (global) time variables, and let Pi(V [fTg) be a set of timing ....

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E. Harel. Temporal analysis of real-time systems. Master's thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.

....use the variable t) as the current time at each state. We refer to this approach as the explicit clock approach, because the only new element is the ability to refer explicitly to the clock. Scattered examples of this method to express timing properties are presented in [PdR82] Ro84] and in [Ha88], PH88] where it is referred to as GCTL. A more systematic exposition of this logic and its applications can be found in [Os90] where it is called RTTL. To compare the two approaches, consider the requirement of a timed response of q to p within at most 3 time units. In the bounded operator ....

E. Harel, Temporal Analysis of Real-time Systems, M.S. Thesis, Weizmann Institute, 1988.

.... that builds on the timing model we have used that of a global, discrete, and asynchronous clock: Os90] uses an explicit clock variable for real time reasoning, and includes many interesting applications; Ko89] introduced the bounded temporal operators we use in our specification language; [Ha88] and [PH88] contrast the interleaving model with a synchronous model; DW90] use finite automata for the specification (and synthesis) of real time systems. More theoretical accounts on specification languages for timed state sequences can be found in [AH89] AH90] and [HLP90] all of which ....

E. Harel, Temporal Analysis of Real-time Systems, M.S. Thesis, Weizmann Institute, 1988.

....state sequences by proving that many conceivable extensions and variations, like additional primitives over time (such as addition) or a dense time domain, result in highly undecidable ( Pi 1 1 hard) theories. It follows from our results that none of the real time logics proposed in [JM86] [Har88], Koy90] and [Ost90] can be decided, which vividly demonstrates that it has not been understood, so far, how expressive a theory of time may be added to reasoning about state sequences without sacrificing decidability. In [AH89] we proposed timed PTL (TPTL) as a natural specification language, ....

....time that are admitted in a logic. We have proved (Case 2) that the addition of time variables causes undecidability. Indeed, using our results and techniques, we can show the Pi 1 1 hardness of various real time logics that have been proposed in the literature, including the logics of [JM86] [Har88], Koy90] and [Ost90] all of which contain addition as a primitive operation on time. In [HLP90] decidability is proved for a real time logic with addition; this logic puts, however, such substantial restrictions on the use of time quantifiers that it is not closed under negation. The real time ....

E. Harel. Temporal analysis of real-time systems. Master's thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.

....and maximal time delays with the transitions. We use the real line as time domain and adapt the definition of timed transition systems that was given for a discrete time domain in [HMP91] Similar notions of transition systems with timing constraints have been defined, for integer time, in [Har88, PH88, HMP90, Ost90] A transition system S = hV; Sigma; Theta; T i consists of four components: 1. a finite set V of variables. 2. a set Sigma of states. Every state oe 2 Sigma is an interpretation of V ; that is, it assigns to every variable x 2 V a value oe(x) in its domain. 3. a subset ....

E. Harel. Temporal analysis of real-time systems. Master's thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.

....depends on the interpretation of the variables x and y. The explicit quantification of variables, however, is typically omitted from first order temporal specifications [PH88, Ost90] Moreover, specification languages are often restricted to formulas with implicit or explicit quantifier prefixes [Har88, HLP90]. The condition (2) is an example that the choice of quantifiers that provides the intended meaning may not be obvious and, indeed, may not correspond to any prefix. In particular, the following quantification of (2) yields a formula that is equivalent to (1) 28x: p now = x) p U 9y: q now ....

....in [Hal91] where it is shown that Presburger arithmetic becomes Pi 1 1 complete with the addition of a single unary predicate. The proof technique we used to show Presburger TPTL undecidable can be applied to many real time specification languages, including the logics RTL [JM86] GCTL [Har88], RTTL [Ost90] and MTL [Koy90] All of these formalisms admit addition over time as a primitive, which renders them undecidable (see [AH90] 4.4 Dense TPTL An alternative way of extending the expressive power of TPTL is to relax the semantics by adopting a dense time domain; that is, between ....

E. Harel. Temporal analysis of real-time systems. Master's thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.

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