  While most of the current synthesis algorithms only focus on
correctness-by-construction, ensuring robustness has remained a challenge.
Hence, in this paper, we address the robust-by-construction synthesis problem
by considering the specifications to be expressed by a robust version of Linear
Temporal Logic (LTL), called robust LTL (rLTL). rLTL has a many-valued
semantics to capture different degrees of satisfaction of a specification,
i.e., satisfaction is a quantitative notion.
  We argue that the current algorithms for rLTL synthesis do not compute
optimal strategies in a non-antagonistic setting. So, a natural question is
whether there is a way of satisfying the specification "better" if the
environment is indeed not antagonistic. We address this question by developing
two new notions of strategies. The first notion is that of adaptive strategies,
which, in response to the opponent's non-antagonistic moves, maximize the
degree of satisfaction. The idea is to monitor non-optimal moves of the
opponent at runtime using multiple parity automata and adaptively change the
system strategy to ensure optimality. The second notion is that of strongly
adaptive strategies, which is a further refinement of the first notion. These
strategies also maximize the opportunities for the opponent to make non-optimal
moves. We show that computing such strategies for rLTL specifications is not
harder than the standard synthesis problem, e.g., computing strategies with LTL
specifications, and takes doubly-exponential time.
