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Repetitive Finite Automata With Translucent Letters

František Mráz, Friedrich Otto

Abstract

Here we propose an extension of the (deterministic and the nondeterministic) finite automaton with translucent letters (DFAwtl and NFAwtl), which lies between these automata and their non-returning variants (that is, the nr-DFAwtl and the nr-NFAwtl). This new model works like a DFAwtl or an NFAwtl, but on seeing the end-of-tape marker, it may change its internal state and continue with its computation instead of just ending it, accepting or rejecting. This new type of automaton is called a repetitive deterministic or nondeterministic finite automaton with translucent letters (RDFAwtl or RNFAwtl). In the deterministic case, the new model is strictly more expressive than the DFAwtl, but less expressive than the nr-DFAwtl, while in the nondeterministic case, the new model is equivalent to the NFAwtl.

Repetitive Finite Automata With Translucent Letters

Abstract

Here we propose an extension of the (deterministic and the nondeterministic) finite automaton with translucent letters (DFAwtl and NFAwtl), which lies between these automata and their non-returning variants (that is, the nr-DFAwtl and the nr-NFAwtl). This new model works like a DFAwtl or an NFAwtl, but on seeing the end-of-tape marker, it may change its internal state and continue with its computation instead of just ending it, accepting or rejecting. This new type of automaton is called a repetitive deterministic or nondeterministic finite automaton with translucent letters (RDFAwtl or RNFAwtl). In the deterministic case, the new model is strictly more expressive than the DFAwtl, but less expressive than the nr-DFAwtl, while in the nondeterministic case, the new model is equivalent to the NFAwtl.
Paper Structure (5 sections, 18 theorems, 35 equations, 2 figures)

This paper contains 5 sections, 18 theorems, 35 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definitions
  3. Comparing the Repetitive Automata to the Non-Repetitive Ones
  4. Closure Properties
  5. Conclusion

Key Result

Proposition 3

$\mathcal{L}({\sf DFAwtl}) \subseteq \mathcal{L}({\sf RDFAwtl})$ and $\mathcal{L}({\sf NFAwtl}) \subseteq \mathcal{L}({\sf RNFAwtl})$.

Figures (2)

  • Figure 1: The diagram describing the RDFAwtl $A_{\vee,c}$. An arrow from a state $q$ to a state $q'$ labeled with a single letter $x$ means that $\tau(q) = \emptyset$ and $q' \in \delta(q,x)$. An arrow labeled with a pair $(\Delta^*,x)$ means that $\tau(q)=\Delta$ and $q'\in \delta(q,x)$.
  • Figure 2: The inclusion relations between the various types of finite automata with translucent letters.

Theorems & Definitions (24)

  • Definition 1
  • Definition 2
  • Proposition 3
  • Example 4
  • Definition 5
  • Theorem 6
  • Definition 7: otto268
  • Definition 8: BiHo_IC284CFY_IJFCS27
  • Theorem 9: otto270
  • Lemma 10
  • ...and 14 more