相关论文: A New Proof of P-time Completeness of Linear Lambd…

Calibration, which establishes the correlation between accuracy and model confidence, is important for LLM development. We design three off-the-shelf calibration methods based on self-consistency (Wang et al., 2022) for math reasoning…

Presented is an inductive formula for computing the sample moments of the distribution of Pearson's sample correlation over permutation of data. These exact formulas for the sample moments suggest the possibility of more precise and…

Vardanyan's Theorems state that $\mathsf{QPL}(\mathsf{PA})$ - the quantified provability logic of Peano Arithmetic - is $\Pi^0_2$ complete, and in particular that this already holds when the language is restricted to a single unary…

In 2014, Darmon and Rotger defined the Garrett-Rankin triple product $p$-adic $L$- function and related it to the image of certain diagonal cycles under the $p$-adic Abel- Jacobi map. We introduce a new $p$-adic triple symbol based on this…

This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…

Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…

In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…

This paper revisits soundness and completeness of proof systems for proving that sets of states in infinite-state labeled transition systems satisfy formulas in the modal mu-calculus. Our results rely on novel results in lattice theory,…

We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…

In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients…

In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…

We introduce a modification of standard Martin-Lof type theory in which we eliminate definitional equality and replace all computation rules by propositional equalities. We show that type checking for such a system can be done in quadratic…

I present a new and reliable method to test the numerical accuracy of NLO calculations based on modern OPP/Generalized Unitarity techniques. A convenient solution to rescue most of the detected numerically inaccurate points is also…

This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize a strong bisimulation between the two…

Let k be a number field, p$\ge$2 a prime and S a set of tame or wild finite places of k. We call K/k a totally S-ramified cyclic p-tower if Gal(K/k)=Z/p^NZ and if S non-empty is totally ramified. Using analogues of Chevalley's formula…

We study coupled logical bisimulation (CLB) to reason about contextual equivalence in the lambda-calculus. CLB originates in a work by Dal Lago, Sangiorgi and Alberti, as a tool to reason about a lambda-calculus with probabilistic…

For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.

We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…

We show that every language in NP has a PCP verifier that tosses $O(\log n)$ random coins, has perfect completeness, and a soundness error of at most $1/\text{poly}(n)$, while making at most $O(\text{poly}\log\log n)$ queries into a proof…

Probabilistic programming languages have recently gained a lot of attention, in particular due to their applications in domains such as machine learning and differential privacy. To establish invariants of interest, many such languages…