The Triple-Pair Construction for Weighted $\omega$-Pushdown Automata

The Triple-Pair Construction for Weighted ω-Pushdown Automata

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...

A Kleene Theorem for Weighted ω-Pushdown Automata

Weighted ω-pushdown automata were introduced as generalization of the classical pushdown automata accepting infinite words by Büchi acceptance. The main result in the proof of the Kleene Theorem is the construction of a weighted ω-pushdown automaton for the ω-algebraic closure of subsets of a continuous star-omega semiring.

Weigthed omega-Restricted One Counter Automata

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-restricted one counter automaton C with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiringsemimodule pair ((S ≪ Σ∗ ≫)n×n, (S ≪ Σω ≫)n) such that the behavior ‖C‖ of C is a component of a solution of this system. In case the basic semiring is B or N∞ we show that...

OpenNWA: A Nested-Word Automaton Library

Nested-word automata (NWAs) are a language formalism that helps bridge the gap between finite-state automata and pushdown automata. NWAs can express some context-free properties, such as parenthesis matching, yet retain all the desirable closure characteristics of finite-state automata. This paper describes OpenNWA, a C++ library for working with NWAs. The library provides the expected automata...

Omega-Continuous Semirings, Algebraich Systems and Pushdown Automata