Automated Generation of Loop Invariants by Recurrence Solving in Theorema
نویسندگان
چکیده
Most of the properties established during program verification are either invariants or depend crucially on invariants. The effectiveness of automated verification of (imperative) programs is therefore sensitive to the ease with which invariants, even trivial ones, can be automatically deduced. We present a method for invariant generation that relies on combinatorial techniques, namely on recurrence solving and variable elimination. The effectiveness of the method is demonstrated on examples. AMS Subject Classification: 33F10, 65G20, 68N30, 68Q60, 68W30
منابع مشابه
Automated Generation of Loop Invariants by Recurrence Solving in Theorema ∗ Presented at 6 International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC04), Timişoara, Romania
Most of the properties established during program verification are either invariants or depend crucially on invariants. The effectiveness of automated verification of (imperative) programs is therefore sensitive to the ease with which invariants, even trivial ones, can be automatically deduced. We present a method for invariant generation that relies on combinatorial techniques, namely on recur...
متن کاملAutomated 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 کاملGeneration of Loop Invariants in Theorema by Combinatorial and Algebraic Methods
When generating verification conditions for a program, one is faced with one major task, namely with the situation when some additional assertions are needed (e.g. loop invariants). These assertions have the property that either they are invariant during execution of the program, or they depend on some other invariant properties. Therefore, automated formal verification is sensitive to the auto...
متن کاملGeneration of Invariants in Theorema
Explicitly stated program invariants can help programmers by identifying program properties that must be preserved when modifying code. In practice, in most of the cases, however, these invariants are usually implicit. In this paper we present an alternative to expecting programmers to fully annotate code with invariants, namely a method for automatically generation of invariants from the progr...
متن کاملPractical Aspects of Imperative Program Verification in Theorema Presented at 5 International Workshop on Symbolic and Numeric Algorithms for Scientific Computing
Approaching the problem of imperative program verification from a practical point of view has certain implications concerning: the style of specifications, the programming language which is used, the help provided to the user for finding appropriate loop invariants, the theoretical frame used for formal verification, the language used for expressing generated verification theorems as well as th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004