Dissertation Abstract First-order Theorem Proving for Program Analysis and Theory Reasoning

Analyzing and verifying computer programs is an important and challenging task. Banks, hospitals, companies, organizations and individuals heavily depend on very complex computer systems, such as Internet, networking, online payment systems, and autonomous devices. These systems are integrated in an even more complicated environment, using various computer devices. Technically, software systems rely on software implementing complicated arithmetic and logical operations over the computer memory. If this software is not reliable, the costs to the economy and society can be huge. Software development practices therefore need rigorous methods ensuring that the program behaves as expected. Formal verification provides a methodology for making reliable and robust systems, by using program properties to hold at intermediate points of the program and using these properties to prove that programs have no errors. Providing such properties manually requires a considerable amount of work by highly skilled personnel and makes verification commercially not viable. Formal verification therefore requires non-trivial automation for generating valid program properties, such as loop invariants. In this thesis we study the use of first-order theorem proving for generating and proving program properties. Our thesis provides a fully automated tool support, called Lingva, for generating quantified invariants of programs over arrays, and shows experimentally that the generated invariants summarize the behavior of the considered loops. Our work is based on the recently introduced symbol elimination method for invariant generation, using a saturation-based