Proof Generation in CDSAT

The main ideas in the CDSAT (Conflict-Driven Satisfiability) framework for SMT are summarized, leading to approaches to proof generation in CDSAT.Comment: In Proceedings PxTP 2021, arXiv:2107.0154

Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo

This articles is a structured bibliography on theorem provers, approaches to theorem proving, and theorem proving applications inspired from Satchmo, the model generation theorem prover developed in the mid 80es of the 20th century at ECRC, the European Computer- Industry Research Centre. Note that the bibliography given in this article is not exhaustive

Larry Wos - Visions of automated reasoning

This paper celebrates the scientific discoveries and the service to the automated reasoning community of Lawrence (Larry) T. Wos, who passed away in August 2020. The narrative covers Larry's most long-lasting ideas about inference rules and search strategies for theorem proving, his work on applications of theorem proving, and a collection of personal memories and anecdotes that let readers appreciate Larry's personality and enthusiasm for automated reasoning

Expectations for Associative-Commutative Unification Speedups in a Multicomputer Environment

An essential element of automated deduction systems is unification algorithms which identify general substitutions and when applied to two expressions, make them identical. However, functions which are associative and commutative, such as the usual addition and multiplication functions, often arise in term rewriting systems, program verification, the theory of abstract data types and logic programming. The introduction to the associative and commutative equality axioms together with standard unification brings with it problems of termination and unreasonably large search spaces. One way around these problems is to remove the troublesome axioms from the system and to employ a unification algorithm which unifies modulo the axioms of associativity and commutativity. Unlike standard unification, the associative-commutative (AC) unification of two expressions can lead to the formation of many most general unifiers. A report is presented on a hybrid AC unification algorithm which has been implemented to run in parallel on an Intel iPSC/

Параллельная обработка данных и знаний методами алгебры кортежей

N-tuple algebra is a mathematical system to formalize n-ary relations. This algebra provides for modelling both data (graphs, n-ary relations, etc.) and knowledge (semantic networks, reasoning models, formulas of propositional and predicate calculi, production systems, ontologies and so on) by the same structures. These structures look like matrices and can be easily processed by parallel algorithms.Алгебра кортежей – математическая система для формализации многоместных отношений. С ее помощью можно моделировать в одних и тех же структурах как данные (графы, многоместные отношения), так и знания (семантические сети, модели рассуждений, формулы исчисления высказываний и предикатов, продукционные системы, онтологии и т.д.). В то же время сами эти структуры имеют матрицеподобную форму, а все алгоритмы их обработки легко распараллеливаются.

Set of support, demodulation, paramodulation: a historical perspective

This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field

On conflict-driven reasoning

Automated formal methods and automated reasoning are interconnected, as formal methods generate reasoning problems and incorporate reasoning techniques. For example, formal methods tools employ reasoning engines to find solutions of sets of constraints, or proofs of conjectures. From a reasoning perspective, the expressivity of the logical language is often directly proportional to the difficulty of the problem. In propositional logic, Conflict-Driven Clause Learning (CDCL) is one of the key features of state-of-the-art satisfiability solvers. The idea is to restrict inferences to those needed to explain conflicts, and use conflicts to prune a backtracking search. A current research direction in automated reasoning is to generalize this notion of conflict-driven satisfiability to a paradigm of conflict-driven reasoning in first-order theories for satisfiability modulo theories and assignments, and even in full first-order logic for generic automated theorem proving. While this is a promising and exciting lead, it also poses formidable challenges

Nagging: A scalable, fault-tolerant, paradigm for distributed search

This paper describes Nagging, a technique for parallelizing search in a heterogeneous distributed computing environment. Nagging exploits the speedup anomaly often observed when parallelizing problems by playing multiple reformulations of the problem or portions of the problem against each other. Nagging is both fault tolerant and robust to long message latencies. In this paper, we show how nagging can be used to parallelize several different algorithms drawn from the artificial intelligence literature, and describe how nagging can be combined with partitioning, the more traditional search parallelization strategy. We present a theoretical analysis of the advantage of nagging with respect to partitioning, and give empirical results obtained on a cluster of 64 processors that demonstrate nagging\u27s effectiveness and scalability as applied to A* search, $alpha beta$ minimax game tree search, and the Davis-Putnam algorithm

Doctor of Philosophy

dissertationTrusted computing base (TCB) of a computer system comprises components that must be trusted in order to support its security policy. Research communities have identified the well-known minimal TCB principle, namely, the TCB of a system should be as small as possible, so that it can be thoroughly examined and verified. This dissertation is an experiment showing how small the TCB for an isolation service is based on software fault isolation (SFI) for small multitasking embedded systems. The TCB achieved by this dissertation includes just the formal definitions of isolation properties, instruction semantics, program logic, and a proof assistant, besides hardware. There is not a compiler, an assembler, a verifier, a rewriter, or an operating system in the TCB. To the best of my knowledge, this is the smallest TCB that has ever been shown for guaranteeing nontrivial properties of real binary programs on real hardware. This is accomplished by combining SFI techniques and high-confidence formal verification. An SFI implementation inserts dynamic checks before dangerous operations, and these checks provide necessary invariants needed by the formal verification to prove theorems about the isolation properties of ARM binary programs. The high-confidence assurance of the formal verification comes from two facts. First, the verification is based on an existing realistic semantics of the ARM ISA that is independently developed by Cambridge researchers. Second, the verification is conducted in a higher-order proof assistant-the HOL theorem prover, which mechanically checks every verification step by rigorous logic. In addition, the entire verification process, including both specification generation and verification, is automatic. To support proof automation, a novel program logic has been designed, and an automatic reasoning framework for verifying shallow safety properties has been developed. The program logic integrates Hoare-style reasoning and Floyd's inductive assertion reasoning together in a small set of definitions, which overcomes shortcomings of Hoare logic and facilitates proof automation. All inference rules of the logic are proven based on the instruction semantics and the logic definitions. The framework leverages abstract interpretation to automatically find function specifications required by the program logic. The results of the abstract interpretation are used to construct the function specifications automatically, and the specifications are proven without human interaction by utilizing intermediate theorems generated during the abstract interpretation. All these work in concert to create the very small TCB