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It can only choose a new state, the result of following the transition. A pushdown automaton (PDA) differs from a finite state machine in two ways: It can use the top of the stack to decide which transition to take. It can manipulate the stack as part of performing a transition. A pushdown automaton reads a given input string from left to right.
The halting problem for a register machine: a finite-state automaton with no inputs and two counters that can be incremented, decremented, and tested for zero. Universality of a nondeterministic pushdown automaton: determining whether all words are accepted. The problem whether a tag system halts.
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]
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to mathematical logic .
A more powerful but still not Turing-complete extension of finite automata is the category of pushdown automata and context-free grammars, which are commonly used to generate parse trees in an initial stage of program compiling. Further examples include some of the early versions of the pixel shader languages embedded in Direct3D and OpenGL ...
LR grammars (also known as deterministic context-free grammars) allow parsing (string recognition) with deterministic pushdown automata (PDA), but they can only describe deterministic context-free languages. Simple LR, Look-Ahead LR grammars are subclasses that allow further simplification of parsing. SLR and LALR are recognized using the same ...
Computer scientists define a language that can be accepted by a pushdown automaton as a Context-free language, which can be specified as a Context-free grammar. The language consisting of strings with equal numbers of 'a's and 'b's, which we showed was not a regular language, can be decided by a push-down automaton.
Nested words over the alphabet = {,, …,} can be encoded into "ordinary" words over the tagged alphabet ^, in which each symbol a from Σ has three tagged counterparts: the symbol a for encoding a call position in a nested word labelled with a, the symbol a for encoding a return position labelled with a, and finally the symbol a itself for representing an internal position labelled with a.