MathematicsFebruary 14, 202638 min read

Markov Decision Processes for Business Workflow State Control: Formalizing the Agentic Company as a State Transition System

How MDPs, Bellman equations, and policy optimization support workflow control, responsibility decomposition, and gate-constrained automation

The agentic company can be modeled as a state-transition system. Business workflows move through discrete states — proposed, validated, approved, executed, completed — with transitions governed by policies balancing efficiency, risk, and human authority. This paper models that process as a Markov Decision Process (MDP), with state dimensions spanning financial, operational, human, risk, and governance factors. We derive Bellman equations for policy optimization, analyze gate-constrained MDP behavior when specific transitions require human approval, and map the MARIA OS decision pipeline to a finite-horizon MDP with responsibility constraints. In tested workflow graphs, policy iteration converged within 12 iterations and yielded 23% throughput improvement over heuristic routing while keeping governance compliance at 100%.

MDPMarkov-decision-processstate-transitionworkflowresponsibility-decompositionpolicy-optimizationBellman-equationvalue-functionagentic-companyMARIA OS
TheoryFebruary 12, 202625 min read

A Formal Model of Responsibility Decomposition Points in Human-AI Decision Systems

Why responsibility is a computable threshold, not a philosophical debate - and how to implement it

Existing AI governance frameworks rely on qualitative guidelines to determine when human oversight is required. This paper formalizes responsibility decomposition as a quantitative threshold problem: we define a Responsibility Demand Function R(d) over decision nodes using five normalized factors - impact, uncertainty, externality, accountability, and novelty - and introduce a decomposition threshold τ that determines when human responsibility must be enforced. A dynamic equilibrium model captures temporal shifts driven by learning and contextual change. The framework is operationalized within MARIA OS gate architecture and validated through reproducible experiments on decision graphs.

responsibility-decompositionformal-methodsdecision-graphdynamic-equilibriumgovernanceMARIA-OScontrol-theoryhuman-ai