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Precise verification of C programs

Most current approaches to software verification are one-sided -- a safety prover will try to prove that a program is safe, while a bug-finding tool will try to find bugs. It is rare to find an analyser that is optimised for both tasks, which is problematic since it is hard to know in advance whether a program you wish to analyse is safe or not. The result of taking a one-sided approach to verification is false alarms: safety provers will often claim that safe programs have errors, while bug-finders will often be unable to find errors in unsafe programs. Orthogonally, many software verifiers are designed for reasoning about idealised programming languages that may not have widespread use. A common assumption made by verification tools is that program variables can take arbitrary integer values, while programs in most common languages use fixed-width bitvectors for their variables. This can have a real impact on the verification, leading to incorrect claims by the verifier. In this thesis we will show that it is possible to analyse C programs without generating false alarms, even if they contain unbounded loops, use non-linear arithmetic and have integer overflows. To do this, we will present two classes of analysis based on underapproximate loop acceleration and second-order satisfiability respectively. Underapproximate loop acceleration addresses the problem of finding deep bugs. By finding closed forms for loops, we show that deep bugs can be detected without unwinding the program and that this can be done without introducing false positives or masking errors. We then show that programs accelerated in this way can be optimised by inlining trace automata to reduce their reachability diameter. This inlining allows acceleration to be used as a viable technique for proving safety, as well as finding bugs. In the second part of the thesis, we focus on using second-order logic for program analysis. We begin by defining second-order SAT: an extension of propositional SAT that allows quantification over functions. We show that this problem is NEXPTIME-complete, and that it is polynomial time reducible to finite-state program synthesis. We then present a fully automatic, sound and complete algorithm for synthesising C programs from a specification written in C. Our approach uses a combination of bounded model checking, explicit-state model checking and genetic programming to achieve surprisingly good performance for a problem with such high complexity. We conclude by using second-order SAT to precisely and directly encode several program analysis problems including superoptimisation, de-obfuscation, safety and termination for programs using bitvector arithmetic and dynamically allocated lists.