It is a routine task to convert a digital circuit to a system of polynomial equations over GF(2). A very well-studied set of tools called “SAT-solvers”, which solve Conjunctive Normal Form logicalsatisfiability problems, can be used to determine if two circuits are equivalent, as is commonly done in computer engineering. An interesting problem in intellectual property is to determine if two cir...

In this paper a new mathematical model is developed for the dynamics between tumor cells, normal cells, immune cells, chemotherapy drug concentration and drug toxicity. Then, the theorem of Lyapunov stability is applied to design treatment strategies for drug protocols that ensure a desired rate of tumor cell kill and push the system to the area with smaller tumor cells. Using of this theorem a...

Algebraic attacks lead to the task of solving polynomial systems over F2. We study recent suggestions of using SAT-solvers for this task. In particular, we develop several strategies for converting the polynomial system to a set of CNF clauses. This generalizes the approach in [4]. Moreover, we provide a novel way of transforming a system over F2e to a (larger) system over F2. Finally, the effi...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

in this paper, we present gauss-sidel and successive over relaxation (sor) iterative methods for finding the approximate solution system of fuzzy sylvester equations (sfse), ax + xb = c, where a and b are two m*m crisp matrices, c is an m*m fuzzy matrix and x is an m*m unknown matrix. finally, the proposed iterative methods are illustrated by solving one example.

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.