Hierarchies for solving Non-linear SMT problems
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چکیده
The desire to make an industrial process cheaper often assumes a high level of automatization of production facilities. Software, although being a set of instructions executed on a machine, is purely created by the human labour. This brings up a natural question. Why would not machines be able to synthesize software and to verify its correctness? Alan Turing proved in 1936 that checking whether the given program will halt on a particular input is undecidable. Thus, verification is not just very hard, but impossible in general. Despite this fact, many teams, including Microsoft Research in Cambridge, are developing techniques and practical tools for performing specific synthesis and verification tasks. Checking Windows drivers and effectively discovering flaws in the operating system is crucial for keeping up with the competition. The bottleneck of the existing frameworks for automatization of the software production is solving satisfiability modulo theories (SMT) problems. The set of verification conditions is encoded as a set of equations. Indeed, we are interested in checking whether an arbitrary boolean combination of non-linear inequalities has a solution. Any feasible solution gives a proof that the desired property holds. However, an infeasible system provides an evidence of an error-prone execution of the software.
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