Minimal Deterministic Finite-state Automata Research Articles

Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications

LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical role in synthesis as well.Therefore, effective resolution of the bottleneck for synthesis requires the conversion to be time and memory performant, and prevent state-space explosion. Current conversion approaches, however, which are based either on explicit-state representation or symbolic-state representation, fail to address these necessities adequately at scale: Explicit-state approaches generate minimal DFA but are slow due to expensive DFA minimization. Symbolic-state representations can be succinct, but due to the lack of DFA minimization they generate such large state spaces that even their symbolic representations cannot compensate for the blow-up.This work proposes a hybrid representation approach for the conversion. Our approach utilizes both explicit and symbolic representations of the state-space, and effectively leverages their complementary strengths. In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck. A comprehensive empirical evaluation on conversion and synthesis benchmarks supports the merits of our hybrid approach.

Extraction of templates from phrases using Sequence Binary Decision Diagrams

AbstractThe extraction of templates such as ‘regard X as Y’ from a set of related phrases requires the identification of their internal structures. This paper presents an unsupervised approach for extracting templates on-the-fly from only tagged text by using a novel relaxed variant of the Sequence Binary Decision Diagram (SeqBDD). A SeqBDD can compress a set of sequences into a graphical structure equivalent to a minimal deterministic finite state automata, but more compact and better suited to the task of template extraction. The main contribution of this paper is a relaxed form of the SeqBDD construction algorithm that enables it to form general representations from a small amount of data. The process of compression of shared structures in the text during Relaxed SeqBDD construction, naturally induces the templates we wish to extract. Experiments show that the method is capable of high-quality extraction on tasks based on verb+preposition templates from corpora and phrasal templates from short messages from social media.

The state complexity of random DFAs

The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random n-state DFAs over a k-symbol alphabet, drawn uniformly from the set [n][n]×[k]×2[n] of all such automata. We show that, with high probability, the latter is αkn+O(nlog⁡n) for a certain explicit constant αk.

Existence of constants in regular splicing languages

In spite of wide investigations of finite splicing systems in formal language theory, basic questions, such as their characterization, remain unsolved. It has been conjectured that a necessary condition for a regular language L to be a splicing language is that L must have a constant in the Schützenberger sense. We prove this longstanding conjecture to be true. The result is based on properties of strongly connected components of the minimal deterministic finite state automaton for a regular splicing language. Using constants of the corresponding languages, we also provide properties of transitive automata and path-automata.