By Lichtenstein O.

This thesis was once performed below the supervision of Prof. A. Pnueli.

This study bargains with decidability, completeness, and extensions of linear

time temporal good judgment. those homes are tested first for a normal type

of versions, that aren't limited to the execution of a selected application

(general validity), after which thought of for a category of versions representing

computations of a given application (validity over program).

The study comprises 3 major components: the 1st bargains with Propositional Temporal common sense (PTL), the second one bargains with mu-Temporal good judgment

(muTL), that is PTL augmented by way of fixpoint operators, and the 3rd half

investigates XCTL that is a model of temporal good judgment that explicitly refers

to a operating clock, to be able to specify actual time homes of reactive

programs.

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**Extra info for Decidability, Completeness, and Extensions of Linear Temporal Logic [PhD Thesis]**

**Sample text**

There is a minor diﬀerence in performing a topological sort on (≤so ∪ ≤po )+ instead of happens-before order. This guarantees consistency with the synchronisation order, which we use in the next lemma. A more signiﬁcant diﬀerence is restricting the execution to all actions before r in ≤t order and updating W (r) to see w, instead of constructing a sequentially consistent completion of the execution. The reason is that sequentially consistent completion might require to insert initialisation actions to the beginning of the execution, hence the original proof does not work as stated, because it assumes that the sequentially consistent completion only adds actions to the “end” of the execution (in terms of ≤t ).

Assemble a set of size measures to be used for the analysis, based on the type of the function argument. 2. e. that the measure gets smaller at the call. Collect the results of the proof attempts in a matrix. 3. Operating only on the matrix from step 2, search for a combination of measures, which form a global termination ordering. This combination, if it exists, can be found in polynomial time. 4. Construct the global termination ordering and, using the proofs of local descent, show that all recursive calls decrease wrt.

The SC- memory model [10] suggests having a special initialisation thread and letting its termination synchronise-with ﬁrst actions of other threads. In our approach, we have tried to stay close to the JMM and instead we deﬁned a new kind of synchronisation action—an initialisation action. These actions belong to a special initialisation thread that contains only the initialisation actions for all variables accessed in the program. The initialisation actions behave like ordinary write actions except they synchronisewith the thread start action of each thread.