Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1406.1090

Tight Bounds for Complementing Parity Automata

Sven Schewe·Thomas Varghese
View original source ↗Read source document ↗Export metadata ↓

Abstract

We follow a connection between tight determinisation and complementation and establish a complementation procedure from parity automata to nondeterministic Büchi automata and prove it to be tight up to an $O(n)$ factor, where $n$ is the size of the nondeterministic parity automaton. This factor does not depend on the number of priorities.

Explore related subjects

cs.FL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sven Schewe, Thomas Varghese. 2014-06-04. Tight Bounds for Complementing Parity Automata. https://doi.org/10.1007/978-3-662-44522-8_42

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↗