Related papers: On Quasi-Interpretations, Blind Abstractions and I…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
Deep Learning methods are renowned for their performances, yet their lack of interpretability prevents them from high-stakes contexts. Recent model agnostic methods address this problem by providing post-hoc interpretability methods by…
We define robust abstractions for synthesizing provably correct and robust controllers for (possibly infinite) uncertain transition systems. It is shown that robust abstractions are sound in the sense that they preserve robust satisfaction…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
We address the problem of analyzing asynchronous event-driven programs, in which concurrent agents communicate via unbounded message queues. The safety verification problem for such programs is undecidable. We present in this paper a…
The system PL permits the translation of abstract proofs of program correctness into programs in a variety of programming languages. A programming language satisfying certain axioms may be the target of such a translation. The system PL…
Mechanistic interpretability aims to reverse engineer neural networks by uncovering which high-level algorithms they implement. Causal abstraction provides a precise notion of when a network implements an algorithm, i.e., a causal model of…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
In this paper we show that property-based abstraction, an established technique originating in software model checking, is a flexible method of controlling polyvariance in program specialisation in a standard online specialisation…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
It was previously shown that control-flow refinement can be achieved by a program specializer incorporating property-based abstraction, to improve termination and complexity analysis tools. We now show that this purpose-built specializer…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
The Bodirsky-Pinsker conjecture asserts a P vs. NP-complete dichotomy for the computational complexity of Constraint Satisfaction Problems (CSPs) of first-order reducts of finitely bounded homogeneous structures. Prominently, two structures…
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This…
The Monniaux Problem in abstract interpretation asks, roughly speaking, whether the following question is decidable: given a program $P$, a safety (\emph{e.g.}, non-reachability) specification $\varphi$, and an abstract domain of invariants…