Lakshmi Manasa

Timed Automata with Integer Resets: Language Inclusion and Expressiveness

In this paper, we consider a syntactic subset of timed automata called integer reset timed automata (IRTA) where resetsare restricted to occur at integral time points. We argue with examples that the notion of global sparse time base used in time triggered architecture and distributed web services can naturally be modelled/specified as IRTA. As our main result, we show that the language inclusion problem

What's decidable about recursive hybrid automata?

L(\mathcal A) \subseteq L(\mathcal{B})

Adding Negative Prices to Priced Timed Games

for a timed automaton

Improved Undecidability Results for Reachability Games on Recursive Timed Automata.

\mathcal A

On Pure Nash Equilibria in Stochastic Games

and an IRTA

Reachability Games on Recursive Hybrid Automata

\mathcal{B}

Updatable Timed Automata with Additive and Diagonal Constraints

is decidable with EXPSPACE complexity. The expressive power and the closure properties of IRTA are also summarized. In particular, the IRTA are (highly succinct but) expressively equivalent to 1-clock deterministic IRTA and they are closed under boolean operations.

Time-Bounded Reachability Problem for Recursive Timed Automata is Undecidable

Recursive hybrid automata generalize recursive state machines in a similar way as hybrid automata generalize state machines. Recursive hybrid automata can be considered as collection of classical hybrid automata with special states that correspond to potentially recursive invocation of hybrid automata from the collection. During each such invocation, the semantics of recursive hybrid automata permits optional passing of the continuous variables using either pass-by-value or pass-by-reference mechanism. This model generalizes recursive timed automata model introduced by Trivedi and Wojtczak and dense-timed pushdown automata by Abdulla, Atig, and Stenman. We study natural reachability problem for recursive hybrid automata. Given the undecidability of this problem for hybrid automata, it is not surprising that the problem remains undecidable without further restrictions. We consider various restrictions of recursive hybrid automata and characterize the boundaries between decidable and undecidable variants.

Revisiting Robustness in Priced Timed Games

Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et al. and Alur, Bernadsky, and Madhusudan independently proposed algorithms to solve PTGs with nonnegative prices under certain divergence restriction over prices. Brihaye, Bruyere, and Raskin later provided a justification for such a restriction by showing the undecidability of the optimal strategy synthesis problem in the absence of this divergence restriction. This problem for PTGs with one clock has long been conjectured to be in polynomial time, however the current best known algorithm, by Hansen, Ibsen-Jensen, and Miltersen, is exponential. We extend this picture by studying PTGs with both negative and positive prices. We refine the undecidability results for optimal strategy synthesis problem, and show undecidability for several variants of optimal reachability cost objectives including reachability cost, time-bounded reachability cost, and repeated reachability cost objectives. We also identify a subclass with bi-valued price-rates and give a pseudo-polynomial (polynomial when prices are nonnegative) algorithm to partially answer the conjecture on the complexity of one-clock PTGs.

Integer Reset Timed Automata: Clock Reduction and Determinizability

We study reachability games on recursive timed automata (RTA) that generalize Alur-Dill timed automata with recursive procedure invocation mechanism similar to recursive state machines. It is known that deciding the winner in reachability games on RTA is undecidable for automata with two or more clocks, while the problem is decidable for automata with only one clock. Ouaknine and Worrell recently proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for several key decision problem related to real-time verification. We revisited games on recursive timed automata with time-bounded restriction in the hope of recovering decidability. However, we found that the problem still remains undecidable for recursive timed automata with three or more clocks. Using similar proof techniques we characterize a decidability frontier for a generalization of RTA to recursive stopwatch automata.