Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Tarski's influence on computer science

The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, modeltheoretic preservation theorems, and algebraic logic; various connections of each with computer science are taken up

Condition/Decision Duality and the Internal Logic of Extensive Restriction Categories

In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to form new conditions, though they only play a supporting role in aiding branching statements choose a branch to follow. On the other hand, in the graphical representation they are typically presented as decisions, intrinsically capable of directing control flow yet mostly oblivious to Boolean combination. While categorical treatments of flowchart languages are abundant, none of them provide a treatment of this dual nature of predicates. In the present paper, we argue that extensive restriction categories are precisely categories that capture such a condition/decision duality, by means of morphisms which, coincidentally, are also called decisions. Further, we show that having these categorical decisions amounts to having an internal logic: Analogous to how subobjects of an object in a topos form a Heyting algebra, we show that decisions on an object in an extensive restriction category form a De Morgan quasilattice, the algebraic structure associated with the (three-valued) weak Kleene logic $\mathbf{K}^w_3$. Full classical propositional logic can be recovered by restricting to total decisions, yielding extensive categories in the usual sense, and confirming (from a different direction) a result from effectus theory that predicates on objects in extensive categories form Boolean algebras. As an application, since (categorical) decisions are partial isomorphisms, this approach provides naturally reversible models of classical propositional logic and weak Kleene logic.Comment: 19 pages, including 6 page appendix of proofs. Accepted for MFPS XXX

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Formalized proof, computation, and the construction problem in algebraic geometry

An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory within a ZFC-like environment

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial