Temporal operator

In linear temporal logic, $\alpha \mathrm{W}\beta$ means $(\alpha \mathrm{U}\beta )\vee G\alpha$. Thus it permits the left operand to hold forever without the right operand ever becoming true, unlike strong until.

In linear temporal logic, $\alpha \mathrm{U}\beta$ holds at position $i$ exactly when some $j\ge i$ satisfies $\beta$ and every position $k$ with $i\le k<j$ satisfies $\alpha$. The witness $j$ must exist. The case $j=i$ imposes no condition on $\alpha$.

The linear temporal logic operator $X\alpha$, true at position $i$ of a path in a transition system exactly when $\alpha$ is true at position $i+1$. Thus $XX\alpha$ tests two positions ahead.