Related papers: The Complexity of Data-Free Nfer
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
This paper presents a specification-guided safety verification method for feedforward neural networks with general activation functions. As such feedforward networks are memoryless, they can be abstractly represented as mathematical…
Satisfiability solvers are increasingly playing a key role in software verification, with particularly effective use in the analysis of security vulnerabilities. String processing is a key part of many software applications, such as…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
We consider here the problem of obtaining reliable, consistent information from inconsistent databases -- databases that do not have to satisfy given integrity constraints. We use the notion of consistent query answer -- a query answer…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer $k\geq 0$, to delete at most $k$ vertices from a given graph so that what remains is a forest. The variant in which the…
We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…
This paper offers a hybrid explainable temporal data processing pipeline, DataFul Explainable MultivariatE coRrelatIonal Temporal Artificial inTElligence (EMeriTAte+DF), bridging numerical-driven temporal data classification with an…
Writing formal specifications for distributed systems is difficult. Even simple consistency requirements often turn out to be unrealizable because of the complicated information flow in the distributed system: not all information is…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
We show that the satisfiability problem for the quantifier-free theory of product structures with the equicardinality relation is in NP. As an application, we extend the combinatory array logic fragment to handle cardinality constraints.…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
Constructing confidence intervals that are simultaneously valid across a class of estimates is central to tasks such as multiple mean estimation, generalization guarantees, and adaptive experimental design. We frame this as an ``error…
Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…