Programming in logic without logic programming

In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by an initial state, sequence of events, and the resulting sequence of subsequent states. In this model-theoretic semantics, reactive rules are the driving force, and logic programs play only a supporting role. In the canonical model, states, actions and other events are represented with timestamps. But in the operational semantics, for the sake of efficiency, timestamps are omitted and only the current state is maintained. State transitions are performed reactively by executing actions to make the consequents of rules true whenever the antecedents become true. This operational semantics is sound, but incomplete. It cannot make reactive rules true by preventing their antecedents from becoming true, or by proactively making their consequents true before their antecedents become true. In this paper, we characterize the notion of reactive model, and prove that the operational semantics can generate all and only such models. In order to focus on the main issues, we omit the logic programming component of the framework.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Path planning algorithm for a car like robot based on MILP method

This project is presents an algorithm for path planning optimal routes mobile robot “like a car” to a target in unknown environment. The proposed algorithm allows a mobile robot to navigate through static obstacles and finding the path in order to reach the target without collision. This algorithm provides the robot the possibility to move from the initial position to the final position (target). The proposed path finding strategy is to use mathematical programming techniques to find the optimal path between to state for mobile robot designed in unknown environment with stationary obstacles. Formulation of the basic problems is to have the vehicle moved from the initial dynamic state to a state without colliding with each other, while at the same time avoiding other stationary obstacles. It is shown that this problem can be rewritten as a linear program with mixed integer / linear constraints that account for the collision avoidance. This approach is that the path optimization can be easily solved using the CPLEX optimization software with AMPL interface / MATLAB. The final phases are the design and build coalitions of linear programs and binary constraints to avoid collision with obstacles by Integer Mixed Linear Program (MILP). The findings of this research have shown that the MILP method can be used in the path planning problem in terms of finding a safe and shortest path. This has been combined with collision avoidance constraints to form a mixed integer linear program, which can be solved by a commercial software package

Assessment of bivariate normality

There are three methods, which are most commonly used to assess the bivariate normality of paired data, two of which are also used to assess the multivariate normality. Nevertheless, none of the methods is very efficient or conclusive in their assessment of bivariate normality. In this thesis we are proposing a new method to test bivariate normality. This new method makes use of a set of if and only if conditions inherent in the theory of bivariate normal distribution. The proposed new method is highly efficient, accurate, and very easy to apply using any available standard statistical software

The Plane-Wave/Super Yang-Mills Duality

We present a self-contained review of the Plane-wave/super-Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large R-charge sector of N=4, D=4 superconformal U(N) gauge theory. This duality is a specification of the usual AdS/CFT correspondence in the "Penrose limit''. The Penrose limit of AdS_5 S^5 leads to the maximally supersymmetric ten dimensional plane-wave (henceforth "the'' plane-wave) and corresponds to restricting to the large R-charge sector, the BMN sector, of the dual superconformal field theory. After assembling the necessary background knowledge, we state the duality and review some of its supporting evidence. We review the suggestion by 't Hooft that Yang-Mills theories with gauge groups of large rank might be dual to string theories and the realization of this conjecture in the form of the AdS/CFT duality. We discuss plane-waves as exact solutions of supergravity and their appearance as Penrose limits of other backgrounds, then present an overview of string theory on the plane-wave background, discussing the symmetries and spectrum. We then make precise the statement of the proposed duality, classify the BMN operators, and mention some extensions of the proposal. We move on to study the gauge theory side of the duality, studying both quantum and non-planar corrections to correlation functions of BMN operators, and their operator product expansion. The important issue of operator mixing and the resultant need for re-diagonalization is stressed. Finally, we study strings on the plane-wave via light-cone string field theory, and demonstrate agreement on the one-loop correction to the string mass spectrum and the corresponding quantity in the gauge theory. A new presentation of the relevant superalgebra is given.Comment: RevTeX 4 format; 91 pages; 7 figures. Prepared for Reviews of Modern Physics. Please send comments to darius, jabbari @ itp.stanford.edu. v3: Minor typos fixe