Selected work

Representative Papers

Cops and robber in graphs with bounded vertex cover number

Feb 07, 2026

This study addresses the problem of bounding the cop number in connected graphs with vertex cover number $k$, offering a structural perspective toward Meyniel’s conjecture. By integrating vertex cover structure analysis, combinatorial optimization, and asymptotic methods, the work establishes the first sublinear upper bound on the cop number parameterized solely by $k$. Specifically, it proves that any connected graph with vertex cover number $k$ has cop number at most $k / 2^{(1 - o(1))\sqrt{\log k}}$. This result breaks away from the conventional framework that depends on the total number of vertices $n$, providing new evidence for Meyniel’s conjecture within structurally restricted graph classes.

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Simplicity Lies in the Eye of the Beholder: A Strategic Perspective on Controllers in Reactive Synthesis

Sep 04, 2025

This work addresses the fundamental question of strategy complexity in reactive controller synthesis: are “succinct” strategies—such as those with finite memory—universally optimal? Traditional approaches often overlook scenario-dependent constraints, leading to overly optimistic assumptions about strategy simplicity. Method: We propose a context-aware framework for evaluating strategy succinctness, integrating game-theoretic modeling, formal verification, and probabilistic strategy optimization to systematically analyze the roles of memory and randomness across diverse synthesis objectives (e.g., safety, liveness). Contribution/Results: Theoretical analysis and empirical evaluation demonstrate that succinct strategies are not universally superior; their efficacy critically depends on task semantics and environmental constraints. In certain settings, memoryless or deterministic strategies are provably insufficient. Our results provide rigorous theoretical criteria and practical guidelines for trading off strategy complexity in controller design, advancing game-based synthesis from a “minimality-first” to an “optimality-adapted” paradigm.

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Mixing Any Cocktail with Limited Ingredients: On the Structure of Payoff Sets in Multi-Objective MDPs and its Impact on Randomised Strategies

Feb 25, 2025

This work investigates the reachability of expected reward vectors in multi-objective Markov decision processes (MDPs), particularly addressing the role of randomized policies when pure policies are insufficient. Using tools from convex analysis, probability theory, and MDP theory, the paper establishes that—under any well-defined multidimensional reward structure—every feasible expected reward vector can be approximated to arbitrary precision via a finite convex combination of pure-policy reward vectors; moreover, in the finite-expectation setting, all feasible reward vectors are exactly attainable. The study rigorously characterizes the convex compactness of the payoff set, precisely quantifies the necessity of randomization, and determines the minimal number of pure policies required for such mixtures—reducing policy complexity from infinite to finite mixtures. These results provide foundational theoretical guarantees for designing approximation algorithms in multi-objective MDPs.

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Recent publications

Latest Papers

Cops and robber in graphs with bounded vertex cover number

Feb 07, 2026

This study addresses the problem of bounding the cop number in connected graphs with vertex cover number $k$, offering a structural perspective toward Meyniel’s conjecture. By integrating vertex cover structure analysis, combinatorial optimization, and asymptotic methods, the work establishes the first sublinear upper bound on the cop number parameterized solely by $k$. Specifically, it proves that any connected graph with vertex cover number $k$ has cop number at most $k / 2^{(1 - o(1))\sqrt{\log k}}$. This result breaks away from the conventional framework that depends on the total number of vertices $n$, providing new evidence for Meyniel’s conjecture within structurally restricted graph classes.

0 citationsRead paper

Simplicity Lies in the Eye of the Beholder: A Strategic Perspective on Controllers in Reactive Synthesis

Sep 04, 2025

This work addresses the fundamental question of strategy complexity in reactive controller synthesis: are “succinct” strategies—such as those with finite memory—universally optimal? Traditional approaches often overlook scenario-dependent constraints, leading to overly optimistic assumptions about strategy simplicity. Method: We propose a context-aware framework for evaluating strategy succinctness, integrating game-theoretic modeling, formal verification, and probabilistic strategy optimization to systematically analyze the roles of memory and randomness across diverse synthesis objectives (e.g., safety, liveness). Contribution/Results: Theoretical analysis and empirical evaluation demonstrate that succinct strategies are not universally superior; their efficacy critically depends on task semantics and environmental constraints. In certain settings, memoryless or deterministic strategies are provably insufficient. Our results provide rigorous theoretical criteria and practical guidelines for trading off strategy complexity in controller design, advancing game-based synthesis from a “minimality-first” to an “optimality-adapted” paradigm.

0 citationsRead paper

Mixing Any Cocktail with Limited Ingredients: On the Structure of Payoff Sets in Multi-Objective MDPs and its Impact on Randomised Strategies

Feb 25, 2025

This work investigates the reachability of expected reward vectors in multi-objective Markov decision processes (MDPs), particularly addressing the role of randomized policies when pure policies are insufficient. Using tools from convex analysis, probability theory, and MDP theory, the paper establishes that—under any well-defined multidimensional reward structure—every feasible expected reward vector can be approximated to arbitrary precision via a finite convex combination of pure-policy reward vectors; moreover, in the finite-expectation setting, all feasible reward vectors are exactly attainable. The study rigorously characterizes the convex compactness of the payoff set, precisely quantifies the necessity of randomization, and determines the minimal number of pure policies required for such mixtures—reducing policy complexity from infinite to finite mixtures. These results provide foundational theoretical guarantees for designing approximation algorithms in multi-objective MDPs.

0 citationsRead paper