Related papers: "ReLIC: Reduced Logic Inference for Composition" f…
Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…
We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…
We present a new version of ReLoC: a relational separation logic for proving refinements of programs with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of ReLoC is its refinement judgment $e…
In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on…
Compositional verification algorithms are well-studied in the context of model checking. Properly selecting components for verification is important for efficiency, yet has received comparatively less attention. In this paper, we address…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…
Composition technologies improve reuse in the development of large-scale complex systems. Safety critical systems require intensive validation and verification activities. These activities should be compositional in order to reduce the…
We consider a modification of the Quantifier Elimination (QE) problem called Partial QE (PQE). In PQE, only a small part of the formula is taken out of the scope of quantifiers. The appeal of PQE is that many verification problems, e.g.…
We study a sound verification method for parametric component-based systems. The method uses a resource logic, a new formal specification language for distributed systems consisting of a finite yet unbounded number of components. The logic…
Large language models (LLMs) are increasingly used to solve complex tasks where they must retrieve and compose many pieces of in-context information in long reasoning chains. For many real-world tasks it is hard to accurately gauge how…
Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…
Recent advancements in test time compute, particularly through the use of verifier models, have significantly enhanced the reasoning capabilities of Large Language Models (LLMs). This generator-verifier approach closely resembles the…
Retrieval-Augmented Generation (RAG) systems typically face constraints because of their inherent mechanism: a simple top-k semantic search [1]. The approach often leads to the incorporation of irrelevant or redundant information in the…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that…
Complex information needs may involve set-compositional queries using conjunction, disjunction, and exclusion, yet it remains unclear whether current retrieval paradigms genuinely satisfy such constraints or exploit `semantic shortcuts'. We…
Distributed systems are critical to reliable and scalable computing; however, they are complicated in nature and prone to bugs. To modularly manage this complexity, network middleware has been traditionally built in layered stacks of…
Quantifier elimination (QE) is an important problem that has numerous applications. Unfortunately, QE is computationally very hard. Earlier we introduced a generalization of QE called $\mathit{partial}$ QE (or PQE for short). PQE allows to…
Traditional logical equivalence checking (LEC) which plays a major role in entire chip design process faces challenges of meeting the requirements demanded by the many emerging technologies that are based on logic models different from…
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…