Related papers: IC3 Modulo Theories via Implicit Predicate Abstrac…
At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is…
Causal abstraction provides a theoretical foundation for mechanistic interpretability, the field concerned with providing intelligible algorithms that are faithful simplifications of the known, but opaque low-level details of black box AI…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
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 propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
This paper introduces the abstraction of max-plus linear (MPL) systems via predicates. Predicates are automatically selected from system matrix, as well as from the specifications under consideration. We focus on verifying time-difference…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Congruence closure procedures are used extensively in automated reasoning and are a core component of most satisfiability modulo theories solvers. However, no known congruence closure algorithms can support any of the expressive logics…
In this paper, we develop a compositional scheme for the construction of continuous approximations for interconnections of infinitely many discrete-time switched systems. An approximation (also known as abstraction) is itself a…
Discrete abstractions of continuous and hybrid systems have recently been the topic of great interest from both the control systems and the computer science communities, because they provide a sound mathematical framework for analysing and…
Efficient planning in continuous state and action spaces is fundamentally hard, even when the transition model is deterministic and known. One way to alleviate this challenge is to perform bilevel planning with abstractions, where a…
IC3, also known as property-directed reachability (PDR), is a commonly-used algorithm for hardware safety model checking. It checks if a state transition system complies with a given safety property. IC3 either returns UNSAFE (indicating…
Commutativity of data structure methods is of ongoing interest, with roots in the database community. In recent years commutativity has been shown to be a key ingredient to enabling multicore concurrency in contexts such as parallelizing…
This paper presents an abstraction-refinement method to synthesize control inputs for a discrete-time piecewise linear system. The controlled system behavior satisfies a finite-word linear-time temporal objective while incurring minimal…
In this paper we consider the problem of configuring partial predicate abstraction that combines two techniques that have been effective in analyzing infinite-state systems: predicate abstraction and fixpoint approximations. A fundamental…
This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x-y<=c) and (+/-x<=c), where x and y are variables values and c is an integer or…
Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We…
Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities…
OpenAI's o3-preview reasoning model exceeded human accuracy on the ARC-AGI-1 benchmark, but does that mean state-of-the-art models recognize and reason with the abstractions the benchmark was designed to test? Here we investigate…
The CEGAR loop in software model checking notoriously diverges when the abstraction refinement procedure does not derive a loop invariant. An abstraction refinement procedure based on an SMT solver is applied to a trace, i.e., a restricted…