  A $d$-limited automaton is a Turing machine that uses only the cells with the
input word (and end-markers) and rewrites symbols only in the first $d$ visits.
This model was introduced by T. Hibbard in 1967 and he showed that $d$-limited
automata recognize context-free languages for each $d \geq 2$. He also proved
that languages recognizable by deterministic $d$-limited automata form a
hierarchy and it was shown later by Pighizzini and Pisoni that it begins with
deterministic context-free languages (DCFLs) (for $d=2$).
  As well-known, DCFLs are widely used in practice, especially in compilers
since they are linear-time recognizable and have the corresponding CF-grammars
subclass (LR$(1)$-grammars). In this paper we present a linear time recognition
algorithm for deterministic $d$-limited automata (in the RAM model) which opens
an opportunity for their possible practical applications. We also generalize
this algorithm to deterministic $d(n)$-limited automata: the extension of
deterministic $d$-limited automata, where $d$ is not a constant, but a function
depending on the input length $n$.
