Related papers: Arithmetics within the Linear Time Hierarchy

We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type…

Signal Temporal Logic (STL) is a formal language for describing a broad range of real-valued, temporal properties in cyber-physical systems. While there has been extensive research on verification and control synthesis from STL…

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…

Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…

There has been a growing interest in extracting formal descriptions of the system behaviors from data. Signal Temporal Logic (STL) is an expressive formal language used to describe spatial-temporal properties with interpretability. This…

The elementary arithmetic operations $+,\cdot,\le$ on integers are well-known to be computable in the weak complexity class $\mathrm{TC}^0$, and it is a basic question what properties of these operations can be proved using only…

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…

Let two static sequences of strings $P$ and $S$, representing prefix and suffix conditions respectively, be given as input for preprocessing. For the query, let two positive integers $k_1$ and $k_2$ be given, as well as a string $T$ given…

The prevailing question in LM performing arithmetic is whether these models learn to truly compute or if they simply master superficial pattern matching. In this paper, we argues for the latter, presenting evidence that LMs act as greedy…

This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may…

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to…

While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…

This paper addresses the issue of specifying, simulating, and verifying reactive systems in rewriting logic. It presents an executable semantics for probabilistic, timed, and spatial concurrent constraint programming -- here called…

The rapid advancement of large language models (LLMs) calls for a rigorous theoretical framework to explain their empirical success. While significant progress has been made in understanding LLM behaviors, existing theoretical frameworks…

This paper presents a novel method of synthesizing a fragment of a timed discrete event system(TDES),introducing a novel linear temporal logic(LTL), called ticked LTL$_f$. The ticked LTL$_f$ is given as an extension to LTL$_f$, where the…

Syntactic NL or succinctly SNL was first introduced in 2017, analogously to SNP, as a ``syntactically''-defined natural subclass of NL (nondeterministic logarithmic-space complexity class) using a restricted form of logical sentences,…

For each $1\leq i \le n$, let $k_i\geq 1$ and let $\Delta_i$ be a set of vertices of a non-degenerate simplex of $k_i+1$ points in $\mathbb{R}^{k_i+1}$. If $A\subseteq [0,1]^{k_1+1}\times \cdots \times [0,1]^{k_n+1}$ is a Lebesgue…

We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure $\delta$ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness (which are…

This paper introduces the 2019 version of \us{}, a novel Constraint Programming framework for floating point verification problems expressed with the SMT language of SMTLIB. SMT solvers decompose their task by delegating to specific…

We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a…