Abstract Formal Specification and Verification of Computational Digital Logic Systems
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Authors
Mertin, Nicholas Frederick Andreas
Date
2025-01-30
Type
thesis
Language
eng
Keyword
Formal methods , Digital systems , Computer architecture
Alternative Title
Abstract
Modern computational digital logic systems, including general-purpose computer processors, make use of increasingly complex control logic and algorithms to manage the flow of data between computational elements. Formal verification methods aim to provide guarantees of correctness for this logic, but their use in practice comes with both combinatorial issues and conceptual challenges in capturing the desired behaviour in the specification language. This problem is exacerbated by the tendency to require behaviour to be specified in terms of the system state trajectory, which is often not a natural setting in which to describe the computational requirements, leading to unnecessary and problematic conceptual distance between the formal specification and the informally understood requirements.
To address these issues, a novel, value-oriented approach to formal verification of these systems is proposed, which permits desired computational behaviour to be specified directly, with a conceptually simple interpretation. This approach is substantiated through an abstract modelling formalism in which computational systems can be formally described and composed from smaller components by compatibly connecting inputs and outputs; the interface of a component is described by an adapted version of polynomial functors, which captures a limited form of dependent typing that is common in real-world digital systems design. A sound but incomplete verification procedure is provided, by translating the description of each system into a novel extension of regular tree grammars which incorporates a limited form of symbolic logic and structured equality constraints, such that language inclusion implies that the system meets the specification. An inductive proof system for such language inclusion between the grammars, again sound but incomplete, is provided to enable algorithmic implementation of verification by proof search. Finally, the system descriptions are assigned category-theoretic semantics, which are used to prove the soundness of the translation to grammars and provide a formal notion of abstracting and concretizing a system between different layers of abstraction.
The result of the thesis is a thorough mathematical foundation for a practical formal verification tool for computational digital logic systems. Remaining work necessary to use such a tool and address the limitations of the underlying theory in its present state is discussed.
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Attribution-NonCommercial-NoDerivatives 4.0 International
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial-NoDerivatives 4.0 International