Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the L* algorithm, introduced by Angluin (1987). The L* algorithm learns deterministic finite-state automata (DFAs) in polynomial time when provided with a minimally adequate teacher. Unfortunately, the L* algorithm can only learn DFAs over finite alphabets, which limits its applicability. In this paper, we extend L* to learn symbolic automata whose transitions use predicates over rational numbers, i.e., over infinite and dense alphabets. Our result makes the L* algorithm applicable to new settings like (real) RGX, and time series. Furthermore, our proposed algorithm for learning each predicate is optimal in the sense that it asks a number of queries to the teacher that is at most linear with respect to the size of their representation.

Multi-agent pathfinding (MAPF) is an NP-hard problem. As such, dense maps may be very hard to solve optimally. In such scenarios, compilation-based approaches, via Boolean satisfiability (SAT) and answer set programming (ASP), have been shown to outperform heuristic-search-based approaches, such as conflict-based search (CBS). In this paper, we propose a new Boolean encoding for MAPF, and show how to implement it in ASP and MaxSAT. A feature that distinguishes our encoding from existing ones is that swap and follow conflicts are encoded using binary clauses, which can be exploited by current conflict-driven clause learning (CDCL) solvers. In addition, the number of clauses used to encode swap and follow conflicts do not depend on the number of agents, allowing us to scale better. For MaxSAT, we study different ways in which we may combine the MSU3 and LSU algorithms for maximum performance. In our experimental evaluation, we used square grids, ranging from 20 x 20 to 50 x 50 cells, and warehouse maps, with a varying number of agents and obstacles. We compared against representative solvers of the state-of-the-art, including the search-based algorithm CBS, the ASP-based solver ASP-MAPF, and the branch-and-cut-and-price hybrid solver, BCP. We observe that the ASP implementation of our encoding, ASP-MAPF2 outperforms other solvers in most of our experiments. The MaxSAT implementation of our encoding, MtMS shows best performance in relatively small warehouse maps when the number of agents is large, which are the instances with closer resemblance to hard puzzle-like problems.

Multi-agent pathfinding (MAPF) is an NP-hard problem. As such, dense maps may be very hard to solve optimally. In such scenarios, compilation-based approaches, via Boolean satisfiability (SAT) and answer set programming (ASP), have proven to be most effective. In this paper, we propose a new encoding for MAPF, which we implement and solve using both ASP and MaxSAT solvers. Our encoding builds on a recent ASP encoding for MAPF but changes the way agent moves are encoded. This allows to represent swap and follow conflicts with binary clauses, which are known to work well along with conflict-based clause learning. For MaxSAT, we study different ways in which we may combine the MSU3 and LSU algorithms for maximum performance. Our results, over grid and warehouse maps, show that the ASP solver scales better when the number of agents is increased on grids with few obstacles, while the MaxSAT solver performs better in scenarios with more obstacles and fewer agents.