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Galois connections are a foundational tool for structuring abstraction in semantics and their use lies at the heart of the theory of abstract interpretation. Yet, mechanization of Galois connections using proof assistants remains limited to…
Static program analysis by abstract interpretation is an efficient method to determine properties of embedded software. One example is value analysis, which determines the values stored in the processor registers. Its results are used as…
Canonical abstraction is a static analysis technique that represents states as 3-valued logical structures, and produces finite abstract systems. Despite providing a finite bound, these abstractions may still suffer from the state explosion…
Probabilistic programming is a powerful abstraction for statistical machine learning. Applying static analysis methods to probabilistic programs could serve to optimize the learning process, automatically verify properties of models, and…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
In this paper we present a dependency graph-based method for computing the various semantics of normal logic programs. Our method employs \textit{conjunction nodes} to unambiguously represent the dependency graph of normal logic programs.…
Algorithmic skeletons are used as building-blocks to ease the task of parallel programming by abstracting the details of parallel implementation from the developer. Most existing libraries provide implementations of skeletons that are…
This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
interpretation is a general methodology for building static analyses of programs. It was introduced by P. and R. Cousot in \cite{cc}. We present, in this paper, an application of a generic abstract interpretation to domain of…
We identify the graph data structure, frontiers, operators, an iterative loop structure, and convergence conditions as essential components of graph analytics systems based on the native-graph approach. Using these essential components, we…
We formalize the semantics of hybrid systems as sets of hybrid trajectories, including those generated by an hybrid transition system. We study the abstraction of hybrid trajectory semantics for verification, static analysis, and…
The paper proposes a new static analysis designed to handle open programs, i.e., fragments of programs, with dynamic pointer-linked data structures - in particular, various kinds of lists - that employ advanced low-level pointer operations.…
In recent years, there has been significant progress in the development and industrial adoption of static analyzers. Such analyzers typically provide a large, if not huge, number of configurable options controlling the precision and…
In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g.…
Many example-guided program synthesis techniques use abstractions to prune the search space. While abstraction-based synthesis has proven to be very powerful, a domain expert needs to provide a suitable abstract domain, together with the…
Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…
The lambda calculus, subject to typing restrictions, provides a syntax for the internal language of cartesian closed categories. This paper establishes a parallel result: staging annotations, subject to named level restrictions, provide a…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…