Process models are, like event data, first-class citizens in most process mining approaches. Several process modeling formalisms have been proposed and used, e.g., Petri nets, BPMN, and process trees. Despite their frequent use, little research addresses the formal properties of process trees and the corresponding potential to improve the efficiency of solving common computational problems. Therefore, in this paper, we propose an invertible state space definition for process trees and demonstrate that the corresponding state space graph is isomorphic to the state space graph of the tree's inverse. Our result supports the development of novel, time-efficient, decomposition strategies for applications of process trees. Our experiments confirm that our state space definition allows for the adoption of bidirectional state space search, which significantly improves the overall performance of state space searches.

Sequential planning in large state space and action space quickly becomes intractable due to combinatorial explosion of the search space. Heuristic methods, like monte-carlo tree search, though effective for large state space, but struggle if action space is large. Pure reinforcement learning methods, relying only on reward signals, needs prohibitively large interactions with the environment to device a viable plan. If the state space, observations and actions can be represented in natural language then Large Language models (LLM) can be used to generate action plans. Recently several such goal-directed agents like Reflexion, CLIN, SayCan were able to surpass the performance of other state-of-the-art methods with minimum or no task specific training. But they still struggle with exploration and get stuck in local optima. Their planning capabilities are limited by the limited reasoning capability of the foundational LLMs on text data. We propose a hybrid agent "neoplanner", that synergizes both state space search with queries to foundational LLM to get the best action plan. The reward signals are quantitatively used to drive the search. A balance of exploration and exploitation is maintained by maximizing upper confidence bounds of values of states. In places where random exploration is needed, the LLM is queried to generate an action plan. Learnings from each trial are stored as entity relationships in text format. Those are used in future queries to the LLM for continual improvement. Experiments in the Scienceworld environment reveals a 124% improvement from the current best method in terms of average reward gained across multiple tasks.

This paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of robust solutions, we propose a new sophistication of A* specially designed to determine the set of robust paths in a state space graph. The behavior of the algorithm is illustrated on a small example. Finally, an axiomatic justification of the refinement of robustness by an OWA criterion is provided.

Choquet expected utility (CEU) is one of the most sophisticated decision criteria used in decision theory under uncertainty. It provides a generalisation of expected utility enhancing both descriptive and prescriptive possibilities. In this paper, we investigate the use of CEU for path-planning under uncertainty with a special focus on robust solutions. We first recall the main features of the CEU model and introduce some examples showing its descriptive potential. Then we focus on the search for Choquet-optimal paths in multivalued implicit graphs where costs depend on different scenarios. After discussing complexity issues, we propose two different heuristic search algorithms to solve the problem. Finally, numerical experiments are reported, showing the practical efficiency of the proposed algorithms.