Related papers: Inductive Satisfiability Certification for Univers…
An operator set is functionally incomplete if it can not represent the full set $\lbrace \neg,\vee,\wedge,\rightarrow,\leftrightarrow\rbrace$. The verification for the functional incompleteness highly relies on constructive proofs. The…
Requirements over strings, commonly represented using natural language (NL), are particularly relevant for software systems due to their heavy reliance on string data manipulation. While individual requirements can usually be analyzed…
We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…
We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
Hallucinations are a persistent problem with Large Language Models (LLMs). As these models become increasingly used in high-stakes domains, such as healthcare and finance, the need for effective hallucination detection is crucial. To this…
This work focuses on effectively generating diverse solutions for satisfiability modulo theories (SMT) formulas, targeting the theories of bit-vectors, arrays, and uninterpreted functions, which is a critical task in software and hardware…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Large Language Models (LLMs) are increasingly deployed to autonomously solve real-world tasks. A key ingredient for this is the LLM Function-Calling paradigm, a widely used approach for equipping LLMs with tool-use capabilities. However, an…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
LTL is frequently used to express specifications in many domains such as embedded systems or business processes. Witnesses can help to understand why an LTL specification is satisfiable, and a number of approaches exist to make…
Motivated by the recent 10 million dollar AIMO challenge, this paper targets the problem of finding all functions conforming to a given specification. This is a popular problem at mathematical competitions and it brings about a number of…
For over two decades Separation Logic has been arguably the most popular framework for reasoning about heap-manipulating programs, as well as reasoning about shared resources and permissions. Separation Logic is often extended to include…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
Arabshahi, Singh, and Anandkumar (2018) propose a method for creating a dataset of symbolic mathematical equations for the tasks of symbolic equation verification and equation completion. Unfortunately, a dataset constructed using the…
We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…