حساب دیفرانسیل و معادلات دیفرانسیل بولی

در این مقاله، ابتدا بخش نظری حساب دیفرانسیل بولی را به همراه مثال‌های کافی تشریح می‌کنیم. سپس به معرفی معادلات دیفرانسیل بولی که شامل مشتقات بولی یک تابع بولی نامعین است، می‌پردازیم و مشاهده می‌شود که متفاوت از یک معادله بولی، جواب یک معادلۀ دیفرانسیل بولی، مجموعه‌ای‎ از توابع بولی است و در نتیجه یک معادلۀ دیفرانسیل بولی امکان توصیف و به‌کارگیری مجموعه‌هایی‎ از توابع بولی را فراهم می‌کند.

the boolean differential calculus and differential equations

the boolean differential calculus is a powerful theory that based on definitions of differentials of boolean variables، differentials of boolean functions and their derivatives، and extended the boolean algebra significantly. definitions and theorems that the boolean differential calculus based on them، allow us to model the changes of function values together with the changes of the values of variables and many other properties of boolean functions. in this paper، first we describe the theory of the boolean differential calculus and present several examples. then، we introduce the boolean differential equations. these equations contain the boolean derivatives of an unknown boolean function. we show that different from a boolean equation، the solution of a boolean differential equation is a set of boolean functions، and therefore، boolean differential equations allow us to describe and handle the sets of boolean functions. in this paper، first we describe the theory of the boolean differential calculus and present several examples. then، we introduce the boolean differential equations. these equations contain the boolean derivatives of an unknown boolean function. we show that different from a boolean equation، the solution of a boolean differential equation is a set of boolean functions، and therefore، boolean differential equations allow us to describe and handle the sets of boolean functions.