Computability of Agentic Systems
Chatavut Viriyasuthee
TL;DR
This paper presents the Quest Graph framework to analyze the computational capabilities of agentic systems, revealing how different abstractions impact their power and efficiency, with implications for system design.
Contribution
It introduces a formal framework for classifying agentic systems' computational power and efficiency, highlighting the effects of various abstractions on their capabilities.
Findings
Base Quest Graph is equivalent to a Turing machine.
FQDP is equivalent to a pushdown automaton.
Reference-augmented QDP can be Turing complete with stateful queries.
Abstract
This paper introduces the Quest Graph, a formal framework for analyzing the capabilities of agentic systems with finite context. We define abstractions that model common reasoning techniques and establish their computational power: the base Quest Graph is equivalent to an unrestricted Turing machine; the forward-only Finite Quest Decision Process (FQDP), despite its wide use, is only equivalent to a pushdown automaton (context-free); and the Reference-Augmented QDP (RQDP) regains Turing completeness only when stateful queries are allowed. Since computability affects efficiency, we then analyze the theoretical efficiency of each model by simulating task dependencies in computation graphs. We show that this computational hierarchy translates to concrete performance trade-offs: reference-augmented (Turing-complete) systems can be exponentially more efficient at simulating complex graphs…
Peer Reviews
Decision·Submitted to ICLR 2026
The reviewer is not particularly familiar with the research domain of computational complexity for language models, except for the more popular work from that subdomain, such as "The Illusion of State in State-Space Models" (Merrill et al., 2024). However, they have a background in deep multi-agent RL and are familiar with MDP variants and agentic systems. ## Clarity - For a theory-heavy paper, the reviewer could follow the paper quite well, which speaks to the logical structure in which the d
# Clarity ## Abstract Overall, the abstract is fairly vague and could be improved. For example: > "Theoretically, we demonstrate that these models form a hierarchy of computational power corresponding to key levels of the formal language hierarchy." > "We then analyze the practical efficiency of each model by simulating task dependencies in computation graphs, revealing that this theoretical hierarchy translates to significant performance trade-offs". (1) Please describe your findings
- The paper connects agent architectures to models from automata theory (FSM, PDA, Turing machine), grounding abstract agentic reasoning in formal computability theory. - The Quest Graph unifies reasoning, memory, and hierarchical task decomposition under one formal model, making it extensible to different types of agents (LLMs, hierarchical RL systems). - The complexity analysis bridges theory and practice by showing the trade-off between computational expressiveness and execution efficiency.
- The framework remains purely theoretical, lacking experimental validation or benchmarking to demonstrate its applicability to real-world agentic systems or LLM-based agents.
The theoretical core is the paper’s main asset. The formalization is careful, with clear separation between agent function and external working memory, and a neat alignment to the formal language hierarchy that makes the progression from LM→QDP→RQDP easy to follow. The hierarchy yields crisp claims: finite-context LMs are only regular; enforcing hierarchical “forward only” structure collapses power to pushdown; adding a reference mechanism with a non-finite tag space restores Turing completeness
First and foremost, There is no empirical validation or case study demonstrating that the complexity separations manifest on realistic agent stacks; without at least small controlled experiments, it is hard to judge how these elegant results transfer outside the formal model. Even without the coverage of experiments, their is a clear lack of discussion around the existing architectures and the theory introduced. The overall presentation undersells where present-day agent systems actually fail an
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Multi-Agent Systems and Negotiation · Computability, Logic, AI Algorithms