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Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained term rewriting. A fundamental question on constrained terms arising there is how to characterize equivalence between them. However, in the current literature only limited progress has been made on this. In this paper, we provide several sound and complete solutions to tackle this problem. Our key idea is the introduction of a novel concept, namely existentially constrained terms, into which the original form of constrained terms can be embedded. We present several syntactic characterizations of equivalence between existentially constrained terms. In particular, we provide two different kinds of complete characterizations: one is designed to facilitate equivalence checking, while the other is intended for theoretical analysis.

Negotiation is a central mechanism of economic exchange, shaping markets, procurement, labor agreements, and resource allocation. It is also a canonical testbed for agentic language models, requiring multi-turn interaction under hidden preferences, strategic communication, and binding constraints. These properties make negotiation hard to evaluate: unlike math or code, it has no intrinsic verifier. Existing LLM negotiation evaluations rely on LLM-vs.-LLM interaction or aggregate outcomes such as deal rate, leaving failures opaque. We introduce Terms-Bench, short for Testbed for Economic Reasoning in Multi-turn Strategy, a Bayesian-game framework that makes the environment itself the verifier by specifying the counterpart's latent type, policy, and payoff structure. We instantiate it in bilateral price negotiation, where the counterpart's private state and simulator policy are hidden from the agent but observable to the evaluator. This turns the counterpart from a black-box opponent into a diagnostic instrument, enabling agent-attributable failure analysis and oracle-reference optimality gaps. Evaluating 13 LLM agents spanning frontier systems from major providers, Terms-Bench turns

The article explores function terms within uniform theories. It examines the uniformity of these theories through an algebraic lens. The paper compares the uniformity of terms and predicates within axiom schemas. It demonstrates the connection between such theories and both field theory and measure theory. The work proposes a novel interpretation of elements as automorphisms of the sets that include them. Additionally, it introduces a method for the localization of elements in relation to one another. Uniform Terms and Local Elements, 2024, msc: 03G30, 03H99 Key words: Terms and predicates, singletons, sections, automorphisms, translation group, Galois correspondence, uniformity and non-uniformity.

Gibbons-Hawking-York (GHY) terms are typically neglected when performing dimensional reductions of gravitational theories. We consider the reduction of such terms for both two-derivative and four-derivative theories in general dimensions. We demonstrate a robust consistency wherein the GHY term in the original, higher-dimensional theory translates directly to the appropriate GHY term in the dimensionally reduced theory. In particular, this gives a novel way of generating such terms for higher-derivative corrections. We carry out this procedure for Gauss-Bonnet, Chern-Simons modified, and $f(R)$ gravities to derive novel boundary terms.

The aim of the article is to provide characterizations of the Haage-rup property for locally compact, second countable groups in terms of approximations of some non-ergodic invariant states by mixing ones for actions on unital $C^*$-algebras one the one hand, and for pairs of tracial von Neumann algebras by mixing binormal states on the other hand.

We search for superspace Chern-Simons-like higher-derivative terms in the low energy effective actions of supersymmetric theories in four dimensions. Superspace Chern-Simons-like terms are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which a gauge potential superfield appears explicitly. We find one class of such four-derivative terms with N=2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally cannot be. These terms are classified by certain Dolbeault cohomology classes on the moduli space. We include a discussion of other examples of terms in the effective action involving global obstructions on the Coulomb branch.

In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's lambda-calculus with resources and based on ideas coming from differential linear logic and differential lambda-calculus. The good properties of this translation wrt. beta-reduction were guaranteed by a coherence relation on resource terms: normalization is "linear and stable" (in the sense of the coherence space semantics of linear logic) wrt. this coherence relation. Such coherence properties are lost when one considers non-deterministic or algebraic extensions of the lambda-calculus (the algebraic lambda-calculus is an extension of the lambda-calculus where terms can be linearly combined). We introduce a "finiteness structure" on resource terms which induces a linearly topologized vector space structure on terms and prevents the appearance of infinite coefficients during reduction, in typed settings.

General relativity (GR) as described in terms of curvature by the Einstein-Hilbert action is dynamically equivalent to theories of gravity formulated in terms of spacetime torsion or non-metricity. This forms what is called the geometrical trinity of gravity. The theories corresponding to this trinity are, apart from GR, the teleparallel (TEGR) and symmetric teleparallel (STEGR) equivalent theories of general relativity, respectively, and their actions are equivalent to GR up to boundary terms $B$. We investigate how the Gibbons-Hawking-York (GHY) boundary term of GR changes under the transition to TEGR and STEGR within the framework of metric-affine gravity. We show that $B$ is the difference between the GHY term of GR and that of metric-affine gravity. Moreover, we show that the GHY term for both TEGR and STEGR must vanish for consistency of the variational problem. Furthermore, our approach allows to extend the equivalence between GR, TEGR and STEGR beyond the Einstein-Hilbert action to any action built out of the curvature two-form, thus establishing the generalized geometrical trinity of gravity. We argue that these results will be particularly useful in view of studying gauge

We prove that every congruence distributive variety has directed Jónsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original Jónsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in CD and CM varieties, respectively. For finite algebras, these absorption theorems have already seen significant applications, but until now, it was not clear if the theorems hold for general algebras as well. Our method also yields a novel proof of a result by P. Lipparini about the existence a chain of terms (which we call Pixley terms) in varieties that are at the same time congruence distributive and $k$-permutable for some $k$.

We derive general expressions for soft terms in supergravity where D-terms contribute significantly to the supersymmetry breaking. Such D-terms can produce large splitting between scalar and fermionic partners in the spectrum. By requiring that supersymmetry breaking sets the cosmological constant to zero, we then parameterize the soft terms when D-terms dominate over F-terms or are comparable to them. We present an application of our results to the split supersymmetry scenario and briefly address the issue of moduli stabilisation.

We study the sequences of numbers corresponding to lambda terms of given sizes, where the size is this of lambda terms with de Bruijn indices in a very natural model where all the operators have size 1. For plain lambda terms, the sequence corresponds to two families of binary trees for which we exhibit bijections. We study also the distribution of normal forms, head normal forms and strongly normalizing terms. In particular we show that strongly normalizing terms are of density 0 among plain terms.

Motivated by symmetry-protected topological phases (SPTs) with both spatial symmetry (e.g., lattice rotation) and internal symmetry (e.g., spin rotation), we propose a class of exotic topological terms, which generalize the well-known Wen-Zee topological terms of quantum Hall systems [X.-G. Wen and A. Zee, Phys. Rev. Lett. 69, 953 (1992)]. These generalized Wen-Zee terms are expressed as wedge product of spin connection and usual gauge fields (1-form or higher) in various dimensions. In order to probe SPT orders, we externally insert "symmetry twists" like domain walls of discrete internal symmetry and disclinations that are geometric defects with nontrivial Riemann curvature. Then, generalized Wen-Zee terms simply tells us how SPTs respond to those symmetry twists. Classifying these exotic topological terms thus leads to a complete classification and characterization of SPTs within the present framework. We also propose SPT low-energy field theories, from which generalized Wen-Zee terms are deduced as topological response actions. Following the Abstract of Wen-Zee paper, our work enriches alternative possibilities of condensed-matter realization of unification of electromagnetism

This paper presents an indirect method for measuring the switch terms of a vector network analyzer (VNA) using at least three reciprocal devices, which do not need to be characterized beforehand. This method is particularly suitable for VNAs that use a three-sampler architecture, which allows for applying first-tier calibration methods based on the error box model. The proposed method was experimentally verified by comparing directly and indirectly measured switch terms and performing a multiline thru-reflect-line (TRL) calibration.

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of order not higher than two (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order four). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to new structure. Our work provides a novel algebraic understanding of the

Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG), have recently drawn considerable attention. Using STGs, terms of exponential size and height can be represented in linear space. Furthermore, the term representation by directed acyclic graphs (dags) can be efficiently simulated. The present paper is the result of an investigation on term unification and matching when the terms given as input are represented using different compression mechanisms for terms such as dags and Singleton Tree Grammars. We describe a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. For the same problem, NP-completeness is obtained when the terms are represented using the more general formalism of Singleton Tree Grammars. For first-order unification and matching polynomial time algorithms are presented, each of them improving previous results for those problems.

We introduce and study semantic capacity of terms. For example, the semantic capacity of artificial intelligence is higher than that of linear regression since artificial intelligence possesses a broader meaning scope. Understanding semantic capacity of terms will help many downstream tasks in natural language processing. For this purpose, we propose a two-step model to investigate semantic capacity of terms, which takes a large text corpus as input and can evaluate semantic capacity of terms if the text corpus can provide enough co-occurrence information of terms. Extensive experiments in three fields demonstrate the effectiveness and rationality of our model compared with well-designed baselines and human-level evaluations.

We present a quantitative, statistical analysis of random lambda terms in the de Bruijn notation. Following an analytic approach using multivariate generating functions, we investigate the distribution of various combinatorial parameters of random open and closed lambda terms, including the number of redexes, head abstractions, free variables or the de Bruijn index value profile. Moreover, we conduct an average-case complexity analysis of finding the leftmost-outermost redex in random lambda terms showing that it is on average constant. The main technical ingredient of our analysis is a novel method of dealing with combinatorial parameters inside certain infinite, algebraic systems of multivariate generating functions. Finally, we briefly discuss the random generation of lambda terms following a given skewed parameter distribution and provide empirical results regarding a series of more involved combinatorial parameters such as the number of open subterms and binding abstractions in closed lambda terms.

Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation. This paper tries to answer questions like: How many terms of a given size are there? What is a "typical" structure of a simply typable term? Despite their ostensible simplicity, these questions still remain unanswered, whereas solutions to such problems are essential for testing compilers and optimizing programs whose expected efficiency depends on the size of terms. Our approach toward the afore-mentioned problems may be later extended to any language with bound variables, i.e., with scopes and declarations. This paper presents two complementary approaches: one, theoretical, uses complex analysis and generating functions, the other, experimental, is based on a generator of lambda-terms. Thanks to de Bruijn indices, we provide three families of formulas for the number of closed lambda terms of a given size and we give four relations between these numbers which have interesting combinatorial interpretations. As a by-product of the counting formulas,