Towards an efficient implementation of a tableau method for reactive safety specifications

In this paper, we will show how to handle a new normal form called terse normal form ($\text{TNF}$), which is crucial to the development of a novel tableau method that solves realizability and synthesis for specifications expressed in a safety fragment of $\text{LTL}$. The construction of these tableaux is based on the conversion of $\text{LTL}$ formulas into $\text{TNF}$, which is one of the most computationally expensive parts of the method. We will explain how to efficiently extract the relevant information required by the tableaux without having to compute the entire $\text{TNF}$ of a safety formula. We present a correct algorithm for carrying out this task as well as its implementation.