Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2306.00135

Optimal Approximate Minimization of One-Letter Weighted Finite Automata

Clara Lacroce·Borja Balle·Prakash Panangaden·Guillaume Rabusseau
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we study the approximate minimization problem of weighted finite automata (WFAs): to compute the best possible approximation of a WFA given a bound on the number of states. By reformulating the problem in terms of Hankel matrices, we leverage classical results on the approximation of Hankel operators, namely the celebrated Adamyan-Arov-Krein (AAK) theory. We solve the optimal spectral-norm approximate minimization problem for irredundant WFAs with real weights, defined over a one-letter alphabet. We present a theoretical analysis based on AAK theory, and bounds on the quality of the approximation in the spectral norm and $\ell^2$ norm. Moreover, we provide a closed-form solution, and an algorithm, to compute the optimal approximation of a given size in polynomial time.

Explore related subjects

cs.FL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Clara Lacroce, Borja Balle, Prakash Panangaden, Guillaume Rabusseau. 2023-05-31. Optimal Approximate Minimization of One-Letter Weighted Finite Automata. https://doi.org/10.1017/s0960129524000276

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Simple grammar bisimilarity, with an application to session type equivalence

We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the grammar, this gives rise to a (single) exponential running time. Previously only a double-exponential algorithm was known. As an application, we provide a conversion from context-free session types to simple grammars whose valuation is linear in the size of the type. In this way, we provide the first polynomial-time algorithm for deciding context-free session type equivalence.

cs.FL↗
arXiv2026

Testing and Learning Symbolic Finite State Machines

Symbolic finite state machines (SFSMs) describe input/output behaviour using guards and output assignments with possibly infinite data domains. We study deterministic and completely specified SFSMs whose guards and output assignments depend only on the current input. We define finite representative input sets that contain witnesses for relevant guard overlaps and separating witnesses for output assignments that differ on those overlaps. Our main theorem shows that language equivalence of the finite instantiations implies language equivalence over the full input domain. This result transfers complete testing methods for deterministic finite state machines (DFSMs) to SFSMs, provided finite sets of admissible guards and output assignments and an upper bound on the number of distinguishable reachable states are known. Under these assumptions, a DFSM learner with complete testing can learn a finite instantiation, which is then lifted to an equivalent SFSM. We establish a bound on the size of representative input sets and give an SMT construction whose correctness and termination hold under stated solver assumptions.

cs.FL↗
arXiv2026

Recognizable Picture Languages: Separating UREC from coUREC via Communication Complexity

We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communication-complexity approach to unambiguous automata of Göös et al. (2022), although its implementation in the setting of picture languages requires substantially different technical ingredients.

cs.FL↗