Kleene algebra with tests (KAT) is an equational system that combines Kleene and Boolean algebras. One can model basic programming constructs and assertions in KAT, which allows for its application in compiler optimization, program transformation and dataflow analysis. To provide semantics for KAT expressions, Kozen first introduced automata on guarded strings, showing that the regular sets of ...

‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are ex...

In this paper, we propose a mean-field game model for the price formation of commodity whose production is subjected to random fluctuations. The generalizes existing deterministic models. Agents seek minimize their average cost by choosing trading rates with that characterized balance between supply and demand. processes are assumed follow stochastic differential equations. Here, show that, lin...

A new line of work [6, 9, 15, 2] demonstrates how differential privacy [8] can be used as a mathematical tool for guaranteeing generalization in adaptive data analysis. Specifically, if a differentially private analysis is applied on a sample S of i.i.d. examples to select a lowsensitivity function f , then w.h.p. f (S) is close to its expectation, although f is being chosen based on the data. ...

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state ...

In a pursuit evasion game, the pursuer tries to capture the evader while the evader tries to prevent this capture. A classical approach is to model this game as an infinite differential game. In this report, we model a pursuit-evasion game as a finite extensive form game, and show that the differential game is a generalization of this game. We prove that a pure-strategy Nash equilibrium always ...

An essential challenge for many developing countries is improvement of water supply system to ensure urban water supply safety and reliability. Penalty, subsidy and water price increase are often considered as the main incentive measures for improving urban water supply system. However, the implementation of these policies is confronting some uncertainties because of the conflicts of involved a...

The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benäım and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to...