Searcharxiv⌕ Search

arXiv subjects

Gabriel Istrate

Publications and source records attributed to Gabriel Istrate.

At least 19 recordsLinked to original sources
arXiv2026

On the Cauchy-Hamel Continuity of Real Functions

We compare several "pathological" notions of continuity that make every additive function continuous. Our goal is to determine which of these notions is best behaved and deserves to be called Cauchy-Hamel continuity. The conclusion is that a bilateral version of a previously introduced notion of Q-continuity seems the most promising candidate. Our work is relevant to the axiomatic foundations of mechanics, specifically to the problem of axiomatically characterizing the parallelogram rule for the composition of forces. It was noted by Darboux that a continuity assumption is needed for such a characterization of the parallelogram rule and that, absent such a continuity axiom, "exotic" physical models based on alternative composition rules may exist. An intriguing question is whether such exotic physical models still possess some weak, residual notion of continuity. The concepts studied in this paper offer a first hint of a response to this question.

math.LO↗
arXiv2026

Undecidability, Chaos and Universality in Arithmetic Terms

Arithmetic terms are finite fixed compositions of additions, subtractions, multiplications, divisions with remainder and exponentiations, containing variables interpreted as natural numbers. They build a well-defined notion of closed formula. It is known that every Kalmar elementary function can be expressed as an arithmetic term. In this paper, one studies the power of expression of the arithmetic terms. By interpreting Hilbert's Tenth Problem in arithmetic terms, it is shown that it is undecidable whether one-variable arithmetic term takes the value $0$, or whether two such terms take or not the same values. An algorithm constructs the arithmetic term representing an arbitrary function, which has been defined by a recurrence rule. This construction has various applications. Functions with chaotic behavior, like the Logistic Map, can be expressed as arithmetic terms. Finally, we construct a Turing complete arithmetic term and we express a Turing universal function by an arithmetic term. A somewhat unexpected application: there is a {\it wise} arithmetic term. It gets (the code of) a sentence, (the code of) a formalized theory and a bound $B$, and after performing a constant number of operations, it outputs (the code of) a proof of the sentence using the given theory if such a proof does exist and its length is less than $B$. Otherwise, it outputs $0$.

math.LO↗
arXiv2026

Hypersphere-Based Restricting Conditions for Colorings of the Euclidean Space

We study colorings of the Euclidean space constrained by \emph{hypersphere forcing conditions}: if an admissible hypersphere, $S_r(p)$, centered at a point $p$ and of radius $r$ contains a monochromatic set of points satisfying a certain property $\mathcal{P}$, then the center of the hypersphere must have that color. These forcing conditions may be restricted in applicability to a specific set of hyperspheres $S_r(p)$. For cardinality-based forcing conditions we prove a general theorem: for countably many colors and any uncountable set of admissible radii $\mathcal{R}$, such a coloring is locally monochromatic on any admissible center set $\Omega \subseteq \mathbb{R}^n$ (hence constant, for connected $\Omega$). For rigid geometric properties (simplex shape, edge-length, volume constraints) we show that forcing conditions alone are insufficient without regularity assumptions. Our main result shows that for colorings satisfying a certain Baire regularity condition rigid geometric properties enforce local monochromaticity and, in the presence of a certain \emph{``uniform cap" condition}, global monochromaticity. Applications include dichotomies for edge-length and volume constraints in terms of $\inf(\mathcal{L})$ and $\inf(\mathcal{V})$, and a comeagerness criterion in the ``all edges in $\mathcal{L}$'' regime.

math.CO↗
arXiv2025

On multiagent online problems with predictions

We study the power of (competitive) algorithms with predictions in a multiagent setting. We introduce a two predictor framework, that assumes that agents use one predictor for their future (self) behavior, and one for the behavior of the other players. The main problem we are concerned with is understanding what are the best competitive ratios that can be achieved by employing such predictors, under various assumptions on predictor quality. As an illustration of our framework, we introduce and analyze a multiagent version of the ski-rental problem. In this problem agents can collaborate by pooling resources to get a group license for some asset. If the license price is not met then agents have to rent the asset individually for the day at a unit price. Otherwise the license becomes available forever to everyone at no extra cost. In the particular case of perfect other predictions the algorithm that follows the self predictor is optimal but not robust to mispredictions of agent's future behavior; we give an algorithm with better robustness properties and benchmark it.

cs.MA↗
arXiv2024

A Language-Theoretic Approach to the Heapability of Signed Permutations

We investigate a signed version of the Hammersley process, a discrete process on words related to a property of integer sequences called heapability (Byers et al., ANALCO 2011). The specific version that we investigate corresponds to a version of this property for signed sequences. We give a characterization of the words that can appear as images the signed Hammersley process. In particular we show that the language of such words is the intersection of two deterministic one-counter languages.

math.CO↗
arXiv2024

Equilibria in multiagent online problems with predictions

We study the power of (competitive) algorithms with predictions in a multiagent setting. To this goal, we introduce a multiagent version of the ski-rental problem. In this problem agents can collaborate by pooling resources to get a group license for some asset. If the license price is not met then agents have to rent the asset individually for the day at a unit price. Otherwise the license becomes available forever to everyone at no extra cost. We investigate the effect of using predictors for self and others' behavior in such a setting, as well as the new equilibria formed in this way.

cs.GT↗
arXiv2023

q-Overlaps in the Random Exact Cover Problem

We prove upper and lower bounds for the threshold of the q-overlap-k-Exact cover problem. These results are motivated by the one-step replica symmetry breaking approach of Statistical Physics, and the hope of using an approach based on that of Mezard et al. (2005) to rigorously prove that for some values of the order parameter the overlap distribution of k-Exact Cover has discontinuous support.

cs.DM↗
arXiv2022

Mechanism Design With Predictions for Obnoxious Facility Location

We study mechanism design with predictions for the obnoxious facility location problem. We present deterministic strategyproof mechanisms that display tradeoffs between robustness and consistency on segments, squares, circles and trees. All these mechanisms are actually group strategyproof, with the exception of the case of squares, where manipulations from coalitions of two agents exist. We prove that these tradeoffs are optimal in the 1-dimensional case.

cs.GT↗
arXiv2022

Some Remarks on Almost Periodic Sequences and Languages

Almost periodicity has been considered in Formal Language Theory in connection with some topics in Symbolic Dynamics. In (P\u{a}un and Marcus, Bulletin of EATCS 53 (1994)) some problems concerning this property are raised. For instance it is asked whether there exists some almost periodic word $\alpha$ such that $Sub(\alpha)$, the set of its finite factors, is context-free non-regular. We answer negatively (even in a stronger form) this question, as well as discussing other related topics.

cs.FL↗
arXiv2021

Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree

A heapable sequence is a sequence of numbers that can be arranged in a "min-heap data structure". Finding a longest heapable subsequence of a given sequence was proposed by Byers, Heeringa, Mitzenmacher, and Zervas (ANALCO 2011) as a generalization of the well-studied longest increasing subsequence problem and its complexity still remains open. An equivalent formulation of the longest heapable subsequence problem is that of finding a maximum-sized binary tree in a given permutation directed acyclic graph (permutation DAG). In this work, we study parameterized algorithms for both longest heapable subsequence as well as maximum-sized binary tree. We show the following results: 1. The longest heapable subsequence problem can be solved in $k^{O(\log{k})}n$ time, where $k$ is the number of distinct values in the input sequence. We introduce the "alphabet size" as a new parameter in the study of computational problems in permutation DAGs. Our result on longest heapable subsequence implies that the maximum-sized binary tree problem in a given permutation DAG is fixed-parameter tractable when parameterized by the alphabet size. 2. We show that the alphabet size with respect to a fixed topological ordering can be computed in polynomial time, admits a min-max relation, and has a polyhedral description. 3. We design a fixed-parameter algorithm with run-time $w^{O(w)}n$ for the maximum-sized binary tree problem in undirected graphs when parameterized by treewidth $w$. Our results make progress towards understanding the complexity of the longest heapable subsequence and maximum-sized binary tree in permutation DAGs from the perspective of parameterized algorithms. We believe that the parameter alphabet size that we introduce is likely to be useful in the context of optimization problems defined over permutation DAGs.

cs.DS↗
arXiv2021

Game-Theoretic Models of Moral and Other-Regarding Agents (extended abstract)

We investigate Kantian equilibria in finite normal form games, a class of non-Nashian, morally motivated courses of action that was recently proposed in the economics literature. We highlight a number of problems with such equilibria, including computational intractability, a high price of miscoordination, and problematic extension to general normal form games. We give such a generalization based on concept of program equilibria, and point out that that a practically relevant generalization may not exist. To remedy this we propose some general, intuitive, computationally tractable, other-regarding equilibria that are special cases Kantian equilibria, as well as a class of courses of action that interpolates between purely self-regarding and Kantian behavior.

cs.GT↗
arXiv2021

Kernelization, Proof Complexity and Social Choice

We display an application of the notions of kernelization and data reduction from parameterized complexity to proof complexity: Specifically, we show that the existence of data reduction rules for a parameterized problem having (a). a small-length reduction chain, and (b). small-size (extended) Frege proofs certifying the soundness of reduction steps implies the existence of subexponential size (extended) Frege proofs for propositional formalizations of the given problem. We apply our result to infer the existence of subexponential Frege and extended Frege proofs for a variety of problems. Improving earlier results of Aisenberg et al. (ICALP 2015), we show that propositional formulas expressing (a stronger form of) the Kneser-Lov\'asz Theorem have polynomial size Frege proofs for each constant value of the parameter k. Previously only quasipolynomial bounds were known (and only for the ordinary Kneser-Lov\'asz Theorem). Another notable application of our framework is to impossibility results in computational social choice: we show that, for any fixed number of agents, propositional translations of the Arrow and Gibbard-Satterthwaite impossibility theorems have subexponential size Frege proofs.

cs.CC↗
arXiv2021

Models we Can Trust: Toward a Systematic Discipline of (Agent-Based) Model Interpretation and Validation

We advocate the development of a discipline of interacting with and extracting information from models, both mathematical (e.g. game-theoretic ones) and computational (e.g. agent-based models). We outline some directions for the development of a such a discipline: - the development of logical frameworks for the systematic formal specification of stylized facts and social mechanisms in (mathematical and computational) social science. Such frameworks would bring to attention new issues, such as phase transitions, i.e. dramatical changes in the validity of the stylized facts beyond some critical values in parameter space. We argue that such statements are useful for those logical frameworks describing properties of ABM. - the adaptation of tools from the theory of reactive systems (such as bisimulation) to obtain practically relevant notions of two systems "having the same behavior". - the systematic development of an adversarial theory of model perturbations, that investigates the robustness of conclusions derived from models of social behavior to variations in several features of the social dynamics. These may include: activation order, the underlying social network, individual agent behavior.

cs.MA↗
arXiv2020

Game-theoretic Models of Moral and Other-Regarding Agents

We investigate Kantian equilibria in finite normal form games, a class of non-Nashian, morally motivated courses of action that was recently proposed in the economics literature. We highlight a number of problems with such equilibria, including computational intractability, a high price of miscoordination, and expensive/problematic extension to general normal form games. We point out that such a proper generalization will likely involve the concept of program equilibrium. Finally we propose some general, intuitive, computationally tractable, other-regarding equilibria related to Kantian equilibria, as well as a class of courses of action that interpolates between purely self-regarding and Kantian behavior.

cs.GT↗
arXiv2020

Being Central on the Cheap: Stability in Heterogeneous Multiagent Centrality Games

We study strategic network formation games in which agents attempt to form (costly) links in order to maximize their network centrality. Our model derives from Jackson and Wolinsky's symmetric connection model, but allows for heterogeneity in agent utilities by replacing decay centrality (implicit in the Jackson-Wolinsky model) by a variety of classical centrality and game-theoretic measures of centrality. We are primarily interested in characterizing the asymptotically pairwise stable networks, i.e. those networks that are pairwise stable for all sufficiently small, positive edge costs. We uncover a rich typology of stability: - we give an axiomatic approach to network centrality that allows us to predict the stable network for a rich set of combination of centrality utility functions, yielding stable networks with features reminiscent of structural properties such as "core periphery" and "rich club" networks. - We show that a simple variation on the model renders it universal, i.e. every network may be a stable network. - We also show that often we can infer a significant amount about agent utilities from the structure of stable networks.

cs.GT↗
arXiv2019

Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm

We analyze the expected running time of WalkSAT, a well-known local search procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT problem. We obtain estimates of this expected running time by reducing the problem to a setting amenable to classical techniques from drift analysis. A crucial ingredient of this reduction is the definition of (new, explosive) hypergraph versions of interacting particle systems, notably of coalescing and annihilating random walks as well as the voter model. The use of these tools allows to show that the expected running time of WalkSAT depends on structural parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.

cs.DS↗
arXiv2019

It's Not Whom You Know, It's What You (or Your Friends) Can Do: Succint Coalitional Frameworks for Network Centralities

We investigate the representation of measures of network centrality using a framework that blends a social network representation with the succint formalism of cooperative skill games. We discuss the expressiveness of the new framework and highlight some of its advantages, including a fixed-parameter tractability result for computing centrality measures under such representations. As an application we introduce new network centrality measures that capture the extent to which neighbors of a certain node can help it complete relevant tasks.

cs.GT↗