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This minor thesis shows a way to optimise a generated oracle to achieve shorter runtimes. Shorter runtimes of test cases allows the execution of more test cases in the same time. The execution of more test cases leads to a higher confidence in the software-quality. Oracles can be derived from specifications. However specifications are used for different purposes and therefore are not necessarily executable. Even if the are executable it might be with only a high runtime. Those two facts come mostly from the use of quantifiers in the logic. If the quantifier-range is not bounded, respectively if the bounds are outside the target language-datatype-limits, the specification is too expressive to be exported into a program. Even if the bounds inside the used datatype-limits, the quantification is represented as a loop which leads to a runtime blowup, especially if quantifiers are nested. This work explains four different possibilities to reduce the execution time of the oracle by manipulating the quantified formular whereas this approach is only applicable if the quantified variables are of type Integer.
E-KRHyper is a versatile theorem prover and model generator for firstorder logic that natively supports equality. Inequality of constants, however, has to be given by explicitly adding facts. As the amount of these facts grows quadratically in the number of these distinct constants, the knowledge base is blown up. This makes it harder for a human reader to focus on the actual problem, and impairs the reasoning process. We extend E-Hyper- underlying E-KRhyper tableau calculus to avoid this blow-up by implementing a native handling for inequality of constants. This is done by introducing the unique name assumption for a subset of the constants (the so called distinct object identifiers). The obtained calculus is shown to be sound and complete and is implemented into the E-KRHyper system. Synthetic benchmarks, situated in the theory of arrays, are used to back up the benefits of the new calculus.
In automated theorem proving, there are some problems that need information on the inequality of certain constants. In most cases this information is provided by adding facts which explicitly state that two constants are unequal. Depending on the number of constants, a huge amount of this facts can clutter the knowledge base and distract the author and readers of the problem from its actual proposition. For most cases it is save to assume that a larger knowledge base reduces the performance of a theorem prover, which is another drawback of explicit inequality facts. Using the unique name assumption in those reasoning tasks renders the introduction of inequality facts obsolete as the unique name assumptions states that two constants are identical iff their interpretation is identical. Implicit handling of non-identical constants makes the problems easier to comprehend and reduces the execution time of reasoning. In this thesis we will show how to integrate the unique name assumption into the E-hyper tableau calculus and that the modified calculus is sound and complete. The calculus will be implemented into the E-KRHyper theorem prover and we will show, by empiric evaluation, that the changed implementation, which is able to use the unique name assumption, is superior to the traditional version of E-KRHyper.
