Finite Automata with Time-Delay Blocks (Extended Version)
For researchers in formal languages and automata theory, this paper introduces a new model with clear expressiveness and complexity results, though it is an incremental extension of finite automata.
This work introduces automata with delay blocks (ADBs), extending finite automata with time delays for output symbols. ADBs strictly subsume regular languages, are incomparable with context-free languages, have decidable emptiness and membership in polynomial time, but undecidable universality, and PSPACE-complete model checking.
The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce \emph{automata with delay blocks} (ADBs), extending finite state automata with variable time delay blocks, for deferring individual transition output symbols, in a discrete-time setting. We show that the ADB languages strictly subsume the regular languages, and are incomparable in expressive power to the context-free languages. We show that ADBs are closed under union, concatenation and Kleene star, and under intersection with regular languages, but not closed under complementation and intersection with other ADB languages. We show that the emptiness and the membership problems are decidable in polynomial time for ADBs, whereas the universality problem is undecidable. Finally we consider the linear-time model checking problem, i.e., whether the language of an ADB is contained in a regular language, and show that the model checking problem is PSPACE-complete.