| Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer, 1995. |
....even (and nonnegative) in order to satisfy the property. Therefore, the set D of the even integers is an invariant. It is not a forward invariant since it does not contain the reachable states 3 and 1. 2. 2 Proof rules for invariants A set D of states is called a strong invariant (or inductive [15]) i# D contains the initial set Y and satisfies x # D for every pair (x, x # ) N with x D. It is easy to verify that a strong invariant contains all reachable states and is therefore a forward invariant. The theory is most easily formulated in terms of sets of states, but for programming ....
....but for programming it is more convenient to use state predicates, i.e. boolean functions on the state space. We therefore identify a state predicate Q with the corresponding set (Q) x # Q(x) Predicate Q is called an invariant if and only if the set (Q) is an invariant. Inspired by [15], we use the following notation to ease our calculations. Recall that K = X, Y, N,P ) with Y X and N X. Let fst and snd be the two projection functions from X X to X. For any set Z and a state function g : X Z, we define g fst : N Z and g snd : N Z. By convention, the ....
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Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer V. 1995.
....the verification of implementation relations. Therefore, there is a need for a property specification language. We will close this gap by defining a temporal logic over executions of I O automata. Existing temporal logics for program verification, like TLA [Lam94] or the logic by Manna Pnueli [MP95] cannot be applied directly in this setting, as executions of I O automata contain explicit actions . Even in TLA, however, actions are merely state changes. Furthermore, existing temporal logics do not consider finite computations. A Priori Verification. Whereas safe implementation ....
....for I O automata. In contrast to existing temporal logics, formulas are evaluated over sequences of alternating states and actions which may be finite. 1. 3 Main Results 9 ffl We investigate the formal relation to existing temporal logics, namely to TLA [Lam94] and the logics by Manna Pnueli [MP95] and Kroger [Kro87] ffl We show how TLS can be used to support the proof of live implementation relations. ffl We develop an abstraction theory which allows us to reduce the verification of both temporal properties and implementation relations to finite state model checking. Even for liveness ....
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Z. Manna and A Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, NY, 1995.
....required to let the program run, we also would like to make explicit that the program fulfils certain properties. The most important technique for reasoning about distributed algorithms is to find invariance conditions that describe the state of the system in every step in every possible execution [9]. Our toolkit allows to formulate such a condition as an assertion that is checked by the simulator in the actually performed execution. In above example, a central property is that there are exactly two messages contained in the network. We can state this as an assertion by rewriting class Prog ....
Zohar Manna and Amir Pnueli. Temporal Verification of Reactive Systems : Safety. Springer, Berlin, Germany, 1995.
....recovered due to appropriate activation of a backup such as the RAT for instance. The correct description of the failure condition should model the fact that the hydraulic system is lost permanently or during a period exceeding some allowed amount of time. Hence we use Linear Temporal Logic (see [16]) operators to model a failure condition. For instance, we could use the two following temporal formulae : P ermanentLoss : 32T otalloss 2TimeStepsLoss : 3(T otalLoss ffiT otalLoss) where 3 is the Future operator, 2 is the always operator and ffi is the next operator. The semantics ot ....
....the activation properties eliminate the unexpected combinations and the control sub system guarantees that the activation properties hold. The synthesis of these verification results is performed thanks to a set of inference rules that preserve the validity of Linear Temporal Logic formulae (see [16]) Necessitation rule : if non temporal formula f is valid in any state of the system then 2f is also valid, Strengthening rule : if formulae 2(g 0 ) f 1 ) f 2 ) and 2(f 0 ) g 0 ) are both valid then formula 2(f 0 ) f 1 ) f 2 ) is also valid Next rule : if formulae 2(f 0 ) f 1 ) f ....
A. Pnueli Z. Manna. Temporal Verification of Reactive Systems - Safety. Springer Verlag, 1995.
....that combines RBAC with states. This allows for talking about things such as the execution history or order of executions, as in [10] while still being much simpler than [10] Temporal logic RBAC is based on temporal first order logic, a logic that has been intensively studied in the literature [12, 13] and comes with standard tools, e.g. 11] A temporal first order signature consists of a set of sorts, a set of function symbols and a set of predicate symbols (each symbol coming with a string of argument sorts and, for function symbols, a result sort) Function and predicate symbols are ....
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
....that is used for the formalization and then develop the various aspects of CA actions. 2 Temporal Logic In this paper, a linear time temporal logic system is used as a specification language for specifying and proving properties of the CA action concept. Lamport [Lam94] Manna and Pnueli [MP91, MP95] and others give a detailed description of the temporal logic framework. In this section, we summarize those aspects needed for formalizing the properties of CA actions. The syntax of temporal logic formulas extends the syntax of formulas in ordinary first order predicate logic by the temporal ....
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, 1995.
....the axiomatization, the program theory can be derived from the program text in a systematic way. Perhaps the most relevant work from mainstream computer science is the specification and verification of reactive systems using temporal logic, in the way pioneered by Pnueli, Manna, and colleagues [49]. The idea is that the computations of reactive systems are infinite sequences, which correspond to models for linear temporal logic. Temporal logic can be used both to develop a system specification, and to axiomatize a programming language. This axiomatization can then be used to systematically ....
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems Safety. Springer-Verlag: Berlin, Germany, 1995.
....of a parallel program. On the other hand, relatively complete deductive systems for proving branching time temporal properties of reactive systems [4] have been recently developed. In recent years, several fully automatic methods for verifying temporal specifications have been introduced, in [6] a tableaux calculus is treated at length; a first introduction to the tableaux method for temporal logic can be seen in [8] However, the scope of these methods is still very limited. Theorem proving procedures for temporal logics have been traditionally based on syntactic manipulations of the ....
Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag, 1995.
.... temporal properties of concurrent heap manipulating programs: We have used the framework to verify temporal properties of concurrent heap manipulating programs in particular, liveness properties, such as the absence of starvation in programs using mutual exclusion, and response properties [13]. We have applied this analysis to programs with an unbounded number of threads. Due to space limitations, the prototype implementation is only discussed in [17, 20] The remainder of this paper is organized as follows: Section 2 gives an overview of the verification method and contrasts it with ....
....#(#v. v) states that globally, each individual that is allocated during program execution is eventually deallocated. Note that the universal quantifier quantifies over individuals of the world in which it is evaluated. This property is an instance of the commonly used Response structure [13, 7], in which an allocation in a world has a deallocation response in some future world. The properties thread.#(at[l lh ] t) # #v.rval[i.next #(at[l lh ] t) # ] t, v) thread.#(#v.at[l lh ] t) #at[l lh ] t) # ] t, v) establish a ranking function for linked data structures ....
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
....the run times are significantly faster (speedups of 50 to 90 percent. We conclude in Section 6. 2 The Framework As a computational model for reactive systems we take the model of fair discrete system (FDS) KP00] which is a slight variation on the model of fair transition system [MP95] and add probabilistic requirements that describe the outcomes of probabilistic selections. We first describe the formal model and the notion of P validity validity with probability 1. We then briefly describe an a simple programming language that allows for probabilistic selections. 2.1 ....
....when S is non probabilistic, that is, when is empty, then the notion of P validity over S coincides with the usual notion of validity over S. 2. 2 Probabilistic SPL All our concrete examples are given in SPL (Simple Programming Language) which is used to represent concurrent programs (e.g. MP95,MAB 94] Every SPL program can be compiled into a PDS in a straightforward manner. In particular, every statement in an SPL program contributes a disjunct to the transition relation. For example, the assignment statement # 0 : x : y 1; # 1 : can be executed when control is at location # ....
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. SpringerVerlag, New York, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems -- Safety. Springer Verlag, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. SpringerVerlag, New York, 1995.
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Z. Manna, A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems --- Safety. Springer Verlag, Berlin (D), 1995.
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MANNA, Z. AND PNUELI, A. 1995. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: safety. Springer, 1995.
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Manna, Z., Pnueli, A.: Temporal verification of reactive systems: safety. Springer (1995)
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer Verlag, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995. *
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, New York, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
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Zohar Manna and Amir Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, New York, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, New York, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995.
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Manna, Z., and Pnueli, A. (1995). Temporal Verification of Reactive Systems: Safety. Springer Verlag.
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Zohar Manna & Amir Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag, New-York, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. SpringerVerlag, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, NY, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, Berlin, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems --- Safety. Springer-Verlag: Berlin, Germany, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995. *
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Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems --- Safety. Springer, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety, pages 272--273. Springer-Verlag, New York, 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: safety. Springer, New York, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer, New York, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems --- Safety. Springer Verlag, Berlin (D), 1995.
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Z. Manna and A. Pnueli. Temporal verification of reactive systems: Safety. Springer-Verlag N.Y., Inc., 1995.
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Manna, Z., and Pnueli, A., Temporal Verification of Reactive Systems: Safety. Springer Verlag, 1995.
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Z. Manna and A. Pnueli, Temporal Verification of Reactive Systems: Safety. New York: Springer, 1995.
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Z. Manna, A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
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Z. Manna, A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
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Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer Verlag, New York, 1995.
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