Software systems are increasingly present in every aspect of our society, as their deployment can be witnessed from seemingly trivial applications of light switches, to critical control systems of nuclear facilities. In the context of critical systems, software faults and errors could potentially lead to detrimental consequences, thus more rigorous methodologies beyond the scope of testing need be applied to software systems. Formal verification, the concept of being able to mathematically prove the correctness of an algorithm with respect to a mathematical formal specification, can indeed help us prevent these failures. A popular specification language for these formal specifications is temporal logic, due to its intuitive, yet precise expressions that can be utilized to both specify and verify fundamental properties pertaining to software systems. Temporal logic can express properties pertaining to safety, liveness, termination, non-termination, and more with regards to various systems such as Windows device drivers, kernel APIs, database servers, etc. This dissertation thus presents automated scalable techniques for verifying expressive temporal logic properties of software systems, specifically those beyond the scope of existing techniques. Furthermore, this work considers the temporal sub-logics fair-CTL, CTL*, and CTL*lp, as verifying these more expressive sub-logics has been an outstanding research problem. We begin building our framework by introducing a novel scalable and high-performance CTL verification technique. Our CTL methodology is unique relative to existing techniques in that it facilitates reasoning about more expressive temporal logics. In particular, it allows us to further introduce various methodologies that allow us to verify fair-CTL, CTL*, and CTL*lp. We support the verification of fair-CTL through a reduction to our CTL model checking technique via the use of infinite non-deterministic branching to symbolically partition fair from unfair executions. For CTL∗, we propose a method that uses an internal encoding which facilitates reasoning about the subtle interplay between the nesting of path and state temporal operators that occurs within CTL∗ proofs. A precondition synthesis strategy is then used over a program transformation which trades nondeterminism in the transition relation for nondeterminism explicit in variables predicting future outcomes when necessary. Finally, we propose a linear-past extension to CTL*, that being CTL*lp, in which the past is linear and each moment in time has a unique past. We support this extension through the use of history variables over our CTL∗ technique. We demonstrate the fully automated implementation of our techniques, and report our bench- marks carried out on code fragments from the PostgreSQL database server, Apache web server, Windows OS kernel, as well as smaller programs demonstrating the expressiveness of fair-CTL, CTL*, and CTL*lp specifications. Together, these novel methodologies lead to a new class of fully automated tools capable of proving crucial properties that no tool could previously prove in the infinite-state setting
