Multi-Turn Tool-Integrated Reasoning (TIR) refers to the process where a model solves a problem by interacting with external tools through multiple rounds to assist reasoning. Although this approach ...

Probabilistic model checking and Markov decision processes (MDPs) form two interlinked branches of formal analysis for systems operating under uncertainty. These techniques offer a mathematical ...

This paper extends the dynamically formulated hidden Markov models to a high-order hidden Markov model (HO-HMM) formulation. In the HO-HMM, the Markovian assumption that the future states (interpreted ...