Deciding Full Branching Time Logic by Program Transformation

We present a method based on logic program transformation, for verifying Computation Tree Logic (CTL*) properties of finite state reactive systems. The finite state systems and the CTL* properties we want to verify, are encoded as logic programs on infinite lists. Our verification method consists of two steps. In the first step we transform the logic program that encodes the given system and the given property, into a monadic ω -program, that is, a stratified program defining nullary or unary predicates on infinite lists. This transformation is performed by applying unfold/fold rules that preserve the perfect model of the initial program. In the second step we verify the property of interest by using a proof method for monadic ω-program

Optimal control theory for unitary transformations

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Out of the schemes studied the square modulus scheme converges fastest. A study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.Comment: 32 pages, 6 figure

Characterising Probabilistic Processes Logically

In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.Comment: 18 page

Speculative Beats Conservative Justification

Abstract. Justifying the truth value of a goal resulting from query evaluation of a logic program corresponds to providing evidence, in terms of a proof, for this truth. In an earlier work we introduced the notion of justification [8] and gave an algorithm for justifying tabled logic programs by post-processing the memo tables created during evaluation. A conservatve justifier such as the one described in that work proceeds in two separate stages: evaluate the truth of literals (that can possibly contribute to the evidence) in the first stage and construct the justification in the next stage. Justifications built in this fashion seldom fail. Whereas for tabled predicates evaluation amounts to a simple table look-up during justification, for non-tabled predicates this amounts to Prolog-style re-execution. In a conservative justifier a non-tabled literal can be re-executed causing unacceptable performance overheads for programs with significant nontabled components: justification time for a single non-tabled literal can become quadratic in its evaluation time! In this paper we introduce the concept of a speculative justifier. In such a justifier we evaluate the truths of literals in tandem with justification. Specifically, we select literals that can possibly provide evidence for the goal’s truth, assume that their truth values correspond to the goal’s and proceed to build a justification for each of them. Since these truths are not computed before hand, justfications produced in this fashion may fail often. On the other hand non-tabled literals are re-executed less often than conservative justifiers. We discuss the subtle efficiency issues that arise in the construction of speculative justifiers. We show how to judiciously balance the different efficiency concerns and engineer a speculative justifier that addresses the performance problem associated with conservative justifiers. We provide experimental evidence of its efficiency and scalability in justifying the results of our XMC model checker.

Research Bulletin / Ag. Econ./1/2007

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Not AvailableNumerous watershed management projects have been undertaken in the recent past by various developmental agencies in different agro-climatic regions having diverse physiographic, climatic and socio-economic conditions. However, the impacts of various watershed interventions have not been objectively evaluated for comparison across the watersheds, states and regions due to lack of availability of appropriate indicators. In this paper, the authors have evolved a large number of useful indicators which have the potential to systematically and scientifically assess the impact of various intervention on bio-physical, socio-economic and sustainability attributes in the watershed management projects being executed across different regions of the country. The main objective of this paper is to sensitize the implementing agencies about the importance of collecting the relevant data during planning, implementation and maintenance phases of the watershed development projects to arrive at useful and logical conclusions and justify public investments. The use of appropriate indicators would also help in critically analysing the relative performance of watershed projects in terms of quantifiable benefits under identical agro-climatic settings as well as across different regions of the country. The results of some of the indicators, tested and evaluated under field conditions have also been presented.Not Availabl

Indigenous Rain Forecasting in Andhra Pradesh

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Research Bulletin. Ag. Econ/2/2007

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Interval Logics and Their Decision Procedures - Part II: A Real-Time Interval Logic

In a companion paper, we presented an interval logic, and showed that it is elementarily decidable. In this paper we extend the logic to allow reasoning about real-time properties of concurrent systems; we call this logic Real-Time Future Interval Logic (RTFIL). We model time by the real numbers, and allow our syntax to state the bounds on the duration of an interval. RTFIL possesses the "real-time interpolation property," which appears to be the natural quantitative counterpart of invariance under finite stuttering. As the main result of this paper, we show that RTFIL is decidable; the decision algorithm is slightly more expensive than for the untimed logic. Our decidability proof is based on the reduction of the satisfiability problem for the logic to the emptiness problem for timed Buchi automata. The latter problem was shown decidable by Alur and Dill in a landmark paper, in which this real-time extension of !-automata was introduced. Finally, we consider an extension of the logic ..