We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised ar...

We take into account the stochastic Boiti–Leon–Manna–Pempinelli equation (SBLMPE), which is perturbed by a multiplicative Brownian motion. By applying He’s semi-inverse method and Riccati mapping method, we can acquire solutions of SBLMPE. Since utilized to explain incompressible liquid in fluid mechanics, acquired may be applied lot fascinating physical phenomena. To address how motion effects...

[1] Apt, K. R.: Logic Programming, Handbook of Theoretical Computer Science (J. van Leeuwen, ed.), Elsevier Science Publishers B.V., 1990. [2] Chang, C.-L. and Lee, R. C.-T.: Symbolic Logic and Mechanical Theorem Proving, Academic Press Inc., 1973. [3] Kowalski, R.: Logic for Problem Solving, North Holland, 1979. [4] Lloyd, J. W.: Foundations of Logic Programming, 2nd Edition, Springer Verlag, ...

We report on a case study in using logical frameworks to support the formalization of programming calculi and their application to deduction-based program synthesis. Within a conservative extension of higher-order logic implemented in the Isabelle system, we derived rules for program development that can simulate those of the deductive tableau proposed by Manna and Waldinger. We have used the r...

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equati...

The hierarchy of properties as overviewed by Manna and Pnueli [18] relates language, topology, $ -automata, and linear temporal logic classifications of properties. We provide new characterisations of this hierarchy in terms of automata with Büchi, co-Büchi, and Streett acceptance condition and in terms of %'&)()& * and +,& (-& * hierarchies. Afterwards, we analyse the complexity of the model c...

We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of sub-level sets of nonlinear functions, generalizes the domain of linear templates introduced by Manna, Sankaranarayanan, and Sipma. In the case of quadratic templates, we use Shor’s semi-definite relaxation to derive safe and computable abstractions of semant...