Practical Aspects of Algebraic Invariant Generation for Loops with Conditionals
نویسندگان
چکیده
We present a method that generates automatically algebraic invariant properties of a loop. The implementation and verification process is done in a prototype verification condition generator for imperative programs. This verification tool is integrated into the overall framework of the Theorema system, which is based on a version of higher order predicate logic and includes verification procedures for functional and rewrite algorithms but also for procedural programs. The main contribution of this paper is the algorithm that generates invariants for loops with conditionals. In the proposed algorithm program analysis is performed in order to transform the code into a form for which algebraic and combinatorial techniques (symbolic summation, variable elimination, polynomial algebra) can be applied to obtain an invariant property. The application of the method is demonstrated in few examples.
منابع مشابه
Automated Invariant Generation by Algebraic Techniques for Imperative Program Verification in Theorema Automated Invariant Generation by Algebraic Techniques for Imperative Program Verification in Theorema
This thesis presents algebraic and combinatorial approaches for reasoning about imperative loops with assignments, sequencing and conditionals. A certain family of loops, called P-solvable, is defined for which the value of each program variable can be expressed as a polynomial of the initial values of variables, the loop counter, and some new variables where there are algebraic dependencies am...
متن کاملA Complete Invariant Generation Approach for P-solvable Loops
We present an algorithm for generating all polynomial invariants of Psolvable loops with assignments and nested conditionals. We prove termination of our algorithm. The proof relies on showing that the dimensions of the prime ideals from the minimal decomposition of the ideals generated at an iteration of our algorithm either remain the same or decrease at the next iteration of the algorithm. O...
متن کاملInvariant Generation for Multi-Path Loops with Polynomial Assignments
Program analysis requires the generation of program properties expressing conditions to hold at intermediate program locations. When it comes to programs with loops, these properties are typically expressed as loop invariants. In this paper we study a class of multi-path program loops with numeric variables, in particular nested loops with conditionals, where assignments to program variables ar...
متن کاملTheoretical, Scientific and Practical Aspects of the Basic Stages of Cad Cam Designing of Centrifugal Pumps
Many theoretical and practical problems arise at different stages of the design/manufacturing process during development of a pump. The experience obtained in pump development proves that the quality of a pump depends on many factors, which should he satisfied to receive good results. At the same time, the theory of engineering design principles exists, which is applicable to designing various ...
متن کاملGeneralized Index-Set Splitting
This paper introduces Index-Set Splitting (ISS), a technique that splits a loop containing several conditional statements into several loops with less complex control flow. Contrary to the classic loop unswitching technique, ISS splits loops when the conditional is loop variant. ISS uses an Index Sub-range Tree (IST) to identify the structure of the conditionals in the loop and to select which ...
متن کامل