Extending fairness expressibility of ECTL+: a tree-style one-pass tableau approach

Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For the specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL^+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL^*, often considered as "the full branching-time logic" overcomes these restrictions on expressing fairness. However, this logic itself, is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for this logic, while it is known that one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more "natural" being more friendly for human understanding. Based on these two considerations, the following problem arises - are there logics that have richer expressiveness than ECTL^+ yet "simpler" than CTL^* for which a one-pass tableau can be developed? In this paper we give a solution to this problem. We present a tree-style one-pass tableau for a sub-logic of CTL^* that we call ECTL^#, which is more expressive than ECTL^+ allowing the formulation of a new range of fairness constraints with "until" operator. The presentation of the tableau construction is accompanied by an algorithm for constructing a systematic tableau, for any given input of admissible branching-time formulae. We prove the termination, soundness and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable for the implementation and for the formulation of sequent calculi, our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL^#, and of a dual sequent calculi

Branching-time logic ECTL# and its tree-style one-pass tableau: Extending fairness expressibility of ECTL+

Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For the specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL⋆, often considered as ‘the full branching-time logic’ overcomes these restrictions on expressing fairness. However, CTL⋆ is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for CTL⋆, while one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more ‘natural’ being more friendly for human understanding. These two considerations lead to the following problem - are there logics that have richer expressiveness than ECTL+, allowing the formulation of a new range of fairness constraints with ‘until’ operator, yet ‘simpler’ than CTL⋆, and for which a one-pass tableau can be developed? Here we give a positive answer to this question, introducing a sub-logic of CTL⋆ called ECTL#, its tree-style one-pass tableau, and an algorithm for obtaining a systematic tableau, for any given admissible branching-time formulae. We prove the termination, soundness and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable for the implementation and for the formulation of sequent calculi. Our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL#, and of a dual sequent calculi

One-pass Context-based Tableaux Systems for CTL and ECTL

When building tableau for temporal logic formulae, applying a two-pass construction, we first check the validity of the given tableaux input by creating a tableau graph, and then, in the second `pass', we check if all the eventualities are satisfied. In one-pass tableaux checking the validity of the input does not require these auxiliary constructions. This paper continues the development of one-pass tableau method for temporal logics introducing tree-style one-pass tableau systems for Computation Tree Logic (CTL) and shows how this can be extended to capture Extended CTL (ECTL). A distinctive feature here is the utilisation, for the core tableau construction, of the concept of a context of an eventuality which forces its earliest fulfilment. Relevant algorithms for obtaining a systematic tableau for these branching-time logics are also defined. We prove the soundness and completeness of the method. With these developments of a tree-shaped one-pass tableau for CTL and ECTL, we have formalisms which are well suited for the automation and are amenable for the implementation, and for the formulation of dual sequent calculi. This brings us one step closer to the application of one pass context based tableaux in certified model checking for a variety of CTL-type branching-time logics

Towards Certified Model Checking for PLTL using One-pass Tableaux

The standard model checking setup analyses whether the given system specification satisfies a dedicated temporal property of the system, providing a positive answer here or a counter-example. At the same time, it is often useful to have an explicit proof that certifies the satisfiability. This is exactly what the {\it certified model checking (CMC)} has been introduced for. The paper argues that one-pass (context-based) tableau for PLTL can be efficiently used in the CMC setting, emphasising the following two advantages of this technique. First, the use of the context in which the eventualities occur, forces them to fulfil as soon as possible. Second, a dual to the tableau sequent calculus can be used to formalise the certificates. The combination of the one-pass tableau and the dual sequent calculus enables us to provide not only counter-examples for unsatisfied properties, but also proofs for satisfied properties that can be checked in a proof assistant. In addition, the construction of the tableau is enriched by an embedded solver, to which we dedicate those (propositional) computational tasks that are costly for the tableaux rules applied solely. The combination of the above techniques is particularly helpful to reason about large (system) specifications

Exclusive pp→nnπ+π+pp \to nn \pi^{+}\pi^{+} reaction at LHC and RHIC

We evaluate differential distributions for the four-body $p p \to n n \pi^+ \pi^+$ reaction. The amplitude for the process is calculated in the Regge approach including many diagrams. We make predictions for possible future experiments at RHIC and LHC energies. Very large cross sections are found which is partially due to interference of a few mechanisms. Presence of several interfering mechanisms precludes extraction of the elastic $\pi^+ \pi^+$ scattering cross section. Absorption effects are estimated. Differential distributions in pseudorapidity, rapidity, invariant two-pion mass, transverse-momentum and energy distributions of neutrons are presented for proton-proton collisions at $\sqrt{s}$ = 500 GeV (RHIC) and $\sqrt{s}$ = 0.9, 2.36 and 7 TeV (LHC). Cross sections with experimental cuts are presented.Comment: 22 pages, 18 figures, calculations have been corrected, new processes added, discussion expanded in print in Phys. Rev.

Economic development of regions during reforming the constitutional and legal model of power delineation in Russian Federation

According to the Russian Federation Constitution, all constituent entities have equal rights. However, equal rights are not synonymous with equality. Equal rights mean legal equality only; in other meanings, they differ significantly from each other. However, if the territorial, demographic and some other differences of the constituent entities of the Russian Federation are the result of objective reasons, and in general do not affect the quality of life of the Russians living there, then the economic differences have more serious consequences. The article makes and attempt to examine the possibilities of economic independence increase in the constituent entities of the Russian Federation. The authors state that the currently existing model of power delimitation is based on the consolidation of the main powers of the federal authorities, while the constituent entities of the Russian Federation are mainly entrusted with financially-intensive powers, which are not always provided with the necessary resources. This matter allows the federal center to accumulate significant financial resources with their subsequent distribution across regions, often in accordance with subjective and non-transparent criteria. In addition, the authors propose the measures to change this situation, in particular, an assessment of power implementation effectiveness at a specific level of power; the ensured provision of the constituent entity powers of the Russian Federation with the necessary resources; use of the system of minimum state social standards

π→lνγ\pi \to l\nu \gamma Form Factors at Two-loop

Within Chiral Perturbation Theory (CHPT) we compute the form factors A, V and $\gamma = A/V$ in the $\pi \to \nu l \gamma$ decay to $O(p^6)$. A and $\gamma$ obtain corrections of order 25%.Comment: Added cut-off dependence discusion, misprints correcte

On the analysis of the pi -> e nu gamma experimental data

The most general amplitude for the radiative pion decay pi -> e nu gamma including terms beyond V-A theory is considered. The experimental constraints on the decay amplitude components are discussed. A model independent presentation of the results of high statistics and high resolution experiments is suggested.Comment: 5 pages, 2 figure