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In computer science, a deterministic automaton is a concept of automata theory where the outcome of a transition from one state to another is determined by the input. [ 1 ] : 41 A common deterministic automaton is a deterministic finite automaton (DFA) which is a finite state machine, where for each pair of state and input symbol there is one ...
The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S 0, S 1, and S 2 (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state for both 0 and 1.
In a non-deterministic Muller automaton, the transition function δ is replaced with a transition relation Δ that returns a set of states and the initial state q 0 is replaced by a set of initial states Q 0. Generally, 'Muller automaton' refers to a non-deterministic Muller automaton. For more comprehensive formalisation look at ω-automaton.
The proposed automaton will accept a word if and only if a time i exists such that it will satisfy the right hand side of Lemma 2. The machine below is described informally. Note that this machine will be a deterministic Muller automaton. The machine contains p+2 deterministic finite automaton and a master controller, where p is the size of A ...
[2] Prior to that it was unknown whether it is possible to perform submatch extraction in one pass on a deterministic finite-state automaton, so this paper was an important advancement. Laurikari described TDFA construction and gave a proof that the determinization process terminates, however the algorithm did not handle disambiguation correctly.
The two are not equivalent for the deterministic pushdown automaton (although they are for the non-deterministic pushdown automaton). The languages accepted by empty stack are those languages that are accepted by final state and are prefix-free: no word in the language is the prefix of another word in the language. [2] [3]
In such an automaton, the set of states can be partitioned into two subsets: one subset forms a deterministic automaton and also contains all the accepting states. For every Büchi automaton, a semi-deterministic Büchi automaton can be constructed such that both recognize the same ω-language. But, a deterministic Büchi automaton may not ...
In automata theory, a co-Büchi automaton is a variant of Büchi automaton. The only difference is the accepting condition: a Co-Büchi automaton accepts an infinite word w {\displaystyle w} if there exists a run, such that all the states occurring infinitely often in the run are in the final state set F {\displaystyle F} .