On Left-Monotone Deterministic Restarting Automata

Jurdziński, Tomasz; Otto, Friedrich; Mráz, František; Plátek, Martin

doi:10.1007/978-3-540-30550-7_21

Cited by 7 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It differs from the standard RRWW-automaton in that rewrite steps of the form u → v are not necessarily length-reducing, but that they are only required to be weight-reducing with respect to some weight function. It is shown in [13] that CFL also coincides with the class of input languages of monotone shrinking RRWW-automata. As a monotone shrinking RRWW-automaton is essentially just an FRR-automaton that only executes 1-con-strained computations, it follows that CFL is contained in the class of languages L I (1, FRR).…”

Section: Constraints Of Word-ordermentioning

confidence: 99%

See 1 more Smart Citation

Free Word-Order and Restarting Automata

Mráz

Otto

Plátek

2014

Fundamenta Informaticae

View full text Add to dashboard Cite

In natural languages with a high degree of word-order freedom, syntactic phenomena like dependencies (subordinations) or valences do not depend on the word-order (or on the individual positions of the individual words). This means that some permutations of sentences of these languages are in some (important) sense syntactically equivalent. Here we study this phenomenon in a formal way. Various types of j-monotonicity for restarting automata can serve as parameters for the degree of word-order freedom and for the complexity of word-order in sentences (languages). Here we combine two types of parameters on computations of restarting automata: the degree of j-monotonicity, and the number of rewrites per cycle. We study these notions formally in order to obtain an adequate tool for modelling and comparing formal descriptions of (natural) languages with different degrees of word-order freedom and word-order complexity.

show abstract

Section: Constraints Of Word-ordermentioning

confidence: 99%

“…In [13] the shrinking RRWW-automaton is introduced (see also [14]). It differs from the standard RRWW-automaton in that rewrite steps of the form u → v are not necessarily length-reducing, but that they are only required to be weight-reducing with respect to some weight function.…”

Section: Constraints Of Word-ordermentioning

confidence: 99%

Free Word-Order and Restarting Automata

Mráz

Otto

Plátek

2014

Fundamenta Informaticae

View full text Add to dashboard Cite

show abstract

“…We now turn to a generalized type of restarting automaton, the shrinking restarting automaton, which was introduced in [26] and further studied in [9][10][11]. A shrinking restarting automaton M is defined just like an RRWW-automaton with the one exception that it is no longer required that each rewrite step u → v of M must be length-reducing.…”

Section: On Shrinking Restarting Automatamentioning

confidence: 99%

“…Analogously, the occurrences of the letter b are rewritten, from left to right, first into b 1 and then into b 2 . However, an occurrence of b can only be rewritten into b 1 (by (11) or (18)) if in that cycle, the rightmost occurrence of the letter a that has already been rewritten happens to be an a 1 (see ( 4) and ( 12)), and an occurrence of b 1 can only be rewritten into b 2 (by (15) or ( 21)) if in that cycle, the rightmost occurrence of the letter a that has already been rewritten happens to be an a 2 (see ( 5) and ( 16)). It follows that s ≥ t, that is, L(M ≥ ) = L ≥ .…”

Section: On Shrinking Restarting Automatamentioning

confidence: 99%

“…Hence, we see that M either deletes the last occurrence of the letter a or the first occurrence of the letter b, which implies that M is monotone. From the indices of the states used, we see that to complete a cycle through the restart operation (11), M must delete the last occurrence of the letter a, if m and n do not have the same parity mod 2, and M must delete the first occurrence of the letter b, if m and n have the same parity mod 2. Indeed, depending on the parities of m and n, we have the following cycles:…”

Section: On Shrinking Restarting Automatamentioning

confidence: 99%

See 1 more Smart Citation

On restarting automata with auxiliary symbols and small window size

Mráz

Otto

2021

RAIRO-Theor. Inf. Appl.

View full text Add to dashboard Cite

Here we show that for monotone RWW- (and RRWW-) automata, window size two is sufficient, both in the nondeterministic as well as in the deterministic case. For the former case, this is done by proving that each context-free language is already accepted by a monotone RWW-automaton of window size two. In the deterministic case, we first prove that each deterministic pushdown automaton can be simulated by a deterministic monotone RWW-automaton of window size three, and then we present a construction that transforms a deterministic monotone RWW-automaton of window size three into an equivalent automaton of the same type that has window size two. Furthermore, we study the expressive power of shrinking RWW- and RRWW-automata the window size of which is just one or two. We show that for shrinking RRWW-automata that are nondeterministic, window size one suffices, while for nondeterministic shrinking RWW-automata, we already need window size two to accept all growing context-sensitive languages. In the deterministic case, shrinking RWW- and RRWW-automata of window size one accept only regular languages, while those of window size two characterize the Church-Rosser languages.

show abstract