Checking order-insensitivity using ternary simulation in synchronous programs

In synchronous systems, new asynchronous distribution schemes are introduced. Properties can be established in order to distribute a program with weak synchronization. This paper deals with automatic verification of the order-insensitive property. Order-insensitivity is an important property introduced in synchronous systems by analogy with delay-insensitivity in asynchronous hardware. An algorithm derived from the Eichelberger ternary algorithm in combinational and sequential switching circuits is given. The new ternary algorithm allows exact detection of order-insensitive property violation. Binary analyses which are conceptually simple and natural, can solve the verification of the order-insensitive property. However, this technique is exponential in the number of state variable computations. By analogy with asynchronous systems, ternary techniques are polynomial in the number of state variable computations. Our goal is to verify if a transition function describing a synchronous program is order-insensitive. Thus, the introduction of an uncertain value in addition to Boolean values allows concretization of the insensitivity introduced by the chaotic order of state variables processing in a distributed way (sequential processing).