On the determinization of event-clock input-driven pushdown automata

TL;DR

This paper extends event-clock input-driven pushdown automata by adding clocks to call-return operations and introduces an optimal determinization method transforming nondeterministic automata into deterministic ones with exponential state and stack symbol growth.

Contribution

It proposes a new determinization procedure for extended event-clock automata with clocks on call-return operations, achieving asymptotic optimality in state and stack symbol complexity.

Findings

Determinization results in automata with 2^{n^2} states and 2^{n^2+k} stack symbols.

The construction is asymptotically optimal for both states and stack symbols.

Extends previous models by including clocks on call-return operations.

Abstract

Input-driven pushdown automata (also known as visibly pushdown automata and as nested word automata) are a subclass of deterministic pushdown automata and a superclass of the parenthesis languages. Nguyen and Ogawa ("Event-clock visibly pushdown automata", SOFSEM 2009) defined a timed extension of these automata under the event-clock model, and showed that this model can be determinized using the method of region construction. This paper defines a further extension of this model with the event clock on the call-return operations, and proposes a new, direct determinization procedure for these automata: an $n$-state nondeterministic automaton with $k$ different clock constraints is transformed to a deterministic automaton with $2^{n^2}$ states, $2^{n^2+k}$ stack symbols and the same clock constraints as in the original automaton. The construction is shown to be asymptotically optimal with respect to both the number of states and the number of stack symbols.