Vijay D'Silva
I am an engineer in the infrastructure security team. I have both foundational and applied research interests. Foundational topics I have studied include automata theory, logic, program analysis and the connections between these three. I currently work on digital forensics and data visualization.
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Buchi, Lindenbaum, Tarski: A Program Analysis Appetizer
Caterina Urban
Proceedings of the International Joint Conference on Artificial Intelligence, AAAI Press (2016) (to appear)
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One can prove that a program program satisfies a correctness property in different ways. The deductive approach uses logic and is automated using decision procedures and proof assistants. The automata-theoretic approach reduces questions about programs to algorithmic questions about automata. In the abstract interpretation approach, programs and their properties are expressed in terms of fixed points in lattices and reasoning uses fixed point approximation techniques. We describe a research programme to establish precise, mathematical correspondences between these approaches and to develop new analyzers using these results. The theoretical tools we use are the theorems of Buchi that relate automata and logic and a construction of Lindenbaum and Tarski for generating lattices from logics. This research has lead to improvements in existing tools and we anticipate further theoretical and practical consequences.
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Automata theory, algorithmic deduction and abstract interpretation provide the foundation behind three approaches to implementing program verifiers. This article is a first step towards a mathematical translation between these approaches. By extending Büchi’s theorem, we show that reachability in a control flow graph can be encoded as satisfiability in an extension of the weak, monadic, second-order logic of one successor. Abstract interpreters are, in a precise sense, sound but incomplete solvers for such formulae. The three components of an abstract interpreter: the lattice, transformers and iteration algorithm, respectively represent a fragment of a first-order theory, deduction in that theory, and second-order constraint propagation. By inverting the Lindenbaum–Tarski construction, we show that lattices used in practice are subclassical first-order theories.
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Abstract Interpretation as Automated Deduction
Caterina Urban
Automated Deduction - CADE 25, Springer International Publishing (2015), pp. 450-464
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Algorithmic deduction and abstract interpretation are two widely used and successful approaches to implementing program verifiers. A major impediment to combining these approaches is that their mathematical foundations and implementation approaches are fundamentally different. This paper presents a new, logical perspective on abstract interpreters that perform reachability analysis using non-relational domains. We encode reachability of a location in a control-flow graph as satisfiability in a monadic, second-order logic parameterized by a first-order theory. We show that three components of an abstract interpreter, the lattice, transformers and iteration algorithm, represent a first-order, substructural theory, parametric deduction and abduction in that theory, and second-order constraint propagation.
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Conflict-Driven Conditional Termination
Caterina Urban
Computer Aided Verification, Springer International Publishing (2015), pp. 271-286
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Conflict-driven learning, which is essential to the performance of sat and smt solvers, consists of a procedure that searches for a model of a formula, and refutation procedure for proving that no model exists. This paper shows that conflict-driven learning can improve the precision of a termination analysis based on abstract interpretation. We encode non-termination as satisfiability in a monadic second-order logic and use abstract interpreters to reason about the satisfiability of this formula. Our search procedure combines decisions with reachability analysis to find potentially non-terminating executions and our refutation procedure uses a conditional termination analysis. Our implementation extends the set of conditional termination arguments discovered by an existing termination analyzer.
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The Correctness-Security Gap in Compiler Optimization
Mathias Payer
Dawn Song
Security and Privacy Workshops (SPW), 2015 IEEE, IEEE, pp. 73-87
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There is a significant body of work devoted to testing, verifying, and certifying the correctness of optimizing compilers. The focus of such work is to determine if source code and optimized code have the same functional semantics. In this paper, we introduce the correctness-security gap, which arises when a compiler optimization preserves the functionality of but violates a security guarantee made by source code. We show with concrete code examples that several standard optimizations, which have been formally proved correct, in-habit this correctness-security gap. We analyze this gap and conclude that it arises due to techniques that model the state of the program but not the state of the underlying machine. We propose a broad research programme whose goal is to identify, understand, and mitigate the impact of security errors introduced by compiler optimizations. Our proposal includes research in testing, program analysis, theorem proving, and the development of new, accurate machine models for reasoning about the impact of compiler optimizations on security.
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