5 papers
Non-Definability of Reachability in Büchi Arithmetic for a Family of Generalized Collatz Maps
Madhav Dhiman, Rohan Pandey
Let and be odd integers with a power of . We study the generalized Collatz map , a one-dimensional piecewise-affine map on the positive intege…
FactorLibrary: From Polynomials to Circuits via Recursive Subgoals
Rohan Pandey, Michael Ruofan Zeng, Weikun K. Zhang +5
Finding minimal arithmetic circuits for polynomials over finite fields is a combinatorially hard problem central to algebraic complexity theory. We formulate it as a reinforcement…
Logical Undefinability of the Generalized Collatz Transition Relation in Büchi Arithmetic
Madhav Dhiman, Rohan Pandey
Let be an odd prime and let be an odd integer. We show that the arbitrary-step transition relation of the generalized Collatz map is not first-order definable in…
Failure Modes of Deep Multi-Agent RL in Asynchronous Pricing: Reproducible Triggers, Trace Diagnostics, and a Partial Fix
Shree Murthy, Rohan Pandey
We study two reproducible failure modes of deep multi-agent reinforcement learning in continuous-time pricing markets: (i) tacit cartel formation between competing DDPG agents, and…
CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning
Weikun K. Zhang, Rohan Pandey, Bhaumik Mehta +5
Motivated by auto-proof generation and Valiant's VP vs. VNP conjecture, we study the problem of discovering efficient arithmetic circuits to compute polynomials, using addition and…