Related papers: Efficient Certified Resolution Proof Checking
We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A…
Many important security properties can be formulated in terms of flows of tainted data, and improved taint analysis tools to prevent such flows are of critical need. Most existing taint analyses use whole-program static analysis, leading to…
Chain-of-thought (CoT) traces are increasingly used both to improve language model capability and to audit model behavior, implicitly assuming that the visible trace remains synchronized with the computation that determines the answer. We…
We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to…
In his 1984 Turing Award lecture, Ken Thompson showed that a compiler could be maliciously altered to insert backdoors into programs it compiles and perpetuate this behavior by modifying any compiler it subsequently builds. Thompson's hack…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
This paper presents the deductive formal verification of high-level properties of control systems with theorem proving, using the Why3 tool. Properties that can be verified with this approach include stability, feedback gain, and…
Formal verification is increasingly recognized as a critical foundation for building reliable software systems. However, the need for specialized expertise to write precise specifications, navigate complex proof obligations, and learn…
We propose a methodology for verifying security properties of network protocols at design level. It can be separated in two main parts: context and requirements analysis and informal verification; and formal representation and procedural…
We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus,…
Several software systems are polyglot; that is, they comprise programs implemented in a combination of programming languages. Verifiers that directly run on mainstream programming languages are currently customized for single languages.…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…
Cryptographic interactive proof systems provide an efficient and scalable means of verifying the results of computation on blockchain. A prover constructs a proof, off-chain, that the execution of a program on a given input terminates with…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
Fact-checking real-world claims often requires reviewing multiple multimodal documents to assess a claim's truthfulness, which is a highly laborious and time-consuming task. In this paper, we present a summarization model designed to…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Proving correctness of distributed or concurrent algorithms is a mind-challenging and complex process. Slight errors in the reasoning are difficult to find, calling for computer-checked proof systems. In order to build computer-checked…
Most software domains rely on compilers to translate high-level code to multiple different machine languages, with performance not too much worse than what developers would have the patience to write directly in assembly language. However,…
Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed…