Decidability of Emptiness Checking in various Alternating Timed Automata and Connections to Timed Logics

In the initial parts of this thesis, we start by approaching the problem of decidability of emptiness of one variable alternating stopwatch automata. We start off by presenting an overview of important results in the field of hybrid systems and useful subclasses and their proofs. Then we go on to alternating timed automata and redo the previously known result that one clock ATA has decidable language emptiness. In the later and more interesting part of the thesis, we then show that language emptiness for one stopwatch ATA is undecidable. We also investigate some connections with timed logics and show that one variable TPTL can be embedded into one clock ATA. We then define a new class of automata called snoopy ATA and show that it is strictly more expressive than one clock ATA and still has decidable language emptiness. We also claim that multiple variable TPTL+F can be embedded into one clock snoopy ATA. But a rigorous proof is not yet developed.