Temporal logic

We have found that temporal logic handles more general cases in a very concise form. The UML activity diagram is another alternative. 

Manna92] Manna, Z., and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems Specification. New York Springer-Verlag. 

Most of the requirements can conveniently be expressed in temporal logic, because certain events are required to happen sometime or never, respectively. Currently, however, the logic is only used to talk about sequences concisely and without writing too many indices. (See Section 5.4.4 for future possibilities.)... 

A convenient formalism to talk about sequences without using many indices is temporal logic. A brief overview for readers unfamiliar with temporal logic follows. For precise definitions, see [MaPn91]. Corresponding to the sequences from the previous subsection, a linear-time logic with discrete, finite time is used. 

The following temporal operators are used (without the usual operator symbols to make the requirements readable for a casual user of temporal logic) ... 

The only exception is that authentication need not work if the message bound N has been reached. Expressing this condition in temporal. logic is probably not the most natural way, but it can be done with a flexible variable counter (i.e., counter may assume different values in different rounds — this is the opposite of a rigid variable), which is formally used to count executions of authentication. 

Formally, one can use the operator EVENTUALLY from temporal logic, for instance, as (Bvalue valid input(id, value)) —> EVENTUALLY output at id). One must then take care in the definition of systems and their runs that all entities somehow finish their current transactions before a run ends, i.e., one cannot consider prefixes of runs. Moreover, such a specification does not reflect the reasonable time in which the output should occur. 

First, if the requirements are restricted to temporal logic, general temporal validity (i.e., the fact that a formula holds for all sequences over the given domain) should trivially imply security validity with every degree of security. 

The text is self-contained with respect to the historical background and cryptologic primitives used. Prior acquaintance with basic notions of complexity theory, information theory, and temporal logic is useful in some chapters. 

The temporal logic of these two questions matches that of the clinical trial (or cohort study) on the one hand and the case - control study on the other. In the clinical trial we manipulate the conditions and observe the effects. In the cohort study no manipulation is involved, but the logic is the same. In the cohort study, on the other hand, sampling is by outcome (effects) and one then tries to work out the possible causes by comparing groups (cases and controls) that differ in terms of effects. 

Interval Temporal Logic, Processor Verification, Executable Specification, Compositionality... 

Our selection of ITL is based on a number of points. It is a flexible notation for both propositional and first-order reasoning about periods of time found in descriptions of hardware and software systems. Unlike most temporal logics, ITL can handle both sequential and parallel composition and offers powerful and extensible specifi-... 

Interval temporal logic is a state based logic which can be used to specify and verify hardware and software systems. Especially it can describe both qualitative and quantitative requirements of systems. Here we only give a brief introduction of ITL. For more details, please refer to B. Moszkowski s papers (Moszkowski 1985, Moszkowski 1986, Moszkowski 1994). 

Cau, A. and Moszkowski, B. (19%) Using PVS for Interval Temporal Logic Proofs, Part 1 The Syntactic and Semantic Encoding. Technical Report, 1996. 

Cau, A., Moszkowski, B. and Zedan, H. (1997) Interval Temporal Logic Proof Checker Manual. In preparation. 

Moszkowski, B. (198S) A Temporal Logic for Multilevel Reasoning About Hardware. IEEE Computer 1985 18 10-19. 

Moszkowski, B. (1986) Executing Temporal Logic Programs. Cambridge Univ. Press, Cambridge, UK, 1986. 

Kroeger, F. (1987) Temporal Logic of Programs. Springer Verlag. 

Subash Shankar is a Ph.D. candidate in the Department of Computer Science at the University of Minnesota. His research interests are in the areas of temporal logics, formal methods, and automated reasoning. 

Bemholtz, 0. (1995), Model (Checking for Branching Time Temporal Logics, PhD thesis, The Technion, Haifa, Israel. 

Clarke, E., Emerson, E. Sistla, A. (1986), Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications , ACM Transactions on Programming Languages and Systems 8(2), 244-263. 

Gerth, R., Peled, D., Vardi, M. Wolper, P. (1995), Simple on-the-fly automatic verification of linear temporal logic, in Protocol Specification Testing and Verification , Chapman Hall, Warsaw, Poland, pp. 3-18. 

Lamport, L. (1980), Sometimes is sometimes not never — on the Temporal Logic of Programs , Proceedings 7th ACM Symposium on Principles of Programming Languages pp. 174-185. 

Symbolic Model Checking for a Discrete Clocked Temporal Logic with Intervals... 

In this paper we present a new model checking algorithm for interval based timed structures and temporal logic formulas. Besides the treatment of time intervals the new algorithm leads to a significant performance gain compared to previous sp-proaches. 

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