(Real-Time and Distributed Real-Time Systems: Theory and Applications) A hybrid automaton H has the following components: Whereas in timed automata, only time is modeled as a real-valued quantity, in hybrid automata multiple variables are real-valued and their behavior is described by differential equations. Hybrid Automata Hybrid automata are a generalization of timed automata.anything that a digital computer with finite memory can compute, can also be computed by a FSA, and by a RNN. Beyond Finite State Automata The ability of RNNs to model FSA should inspire great confidence in these systems as FSA represent the computational limits of digital computers with finite memory resources.(Handbook on Neural Information Processing) The mathematical formulation of the FSA M is a 6-tuple and can be defined by: where Q. Large portion of discrete processes can be modeled by deterministic finite-state automata (DFA). Finite State Automata FSA have a finite number of input and output symbols, and a finite number of internal states.If there are pairs of current state and input for which the transition function specifies two or more next states or no next state at all, the state machine is nondeterministic.* A nondeterministic FSM can be transformed into an equivalent deterministic FSM. means if the FSM is in state s t and reads input k, then it will move to state s.Ī state machine is deterministic, if the transition function specifies exactly one next state for every pair of current state and input. for a given state s t e S and a given input k e I. The transition function, d, determines the next state s. A subset of the states can be defined as accepting states. Initially, the FSM is in the start state, s 0. At any time, the FSM is in exactly one state, s. An FSM has a finite set of states S =, an input alphabet I, an output alphabet O, and a state transition function d:S x I ^ S. A finite state machine (FSM) can be used as a formal representation of an even-driven (reactive) system.