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Summary
This summary is machine-generated.

This study introduces a dynamic data structure for automata theory, enabling efficient online acceptance checking of streamed input words for timed automata. The structure achieves an amortized update time of O(log n) per symbol for one-clock timed automata.

Keywords:
Data streamDynamic data structureTimed automata

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Area of Science:

  • Theoretical Computer Science
  • Automata Theory
  • Formal Languages
  • Algorithm Design

Background:

  • The classical membership problem in automata theory determines if an input word is accepted by a given automaton.
  • Streaming data and dynamic updates present challenges for traditional static automaton analysis.
  • Timed automata incorporate time constraints, adding complexity to acceptance problems.

Purpose of the Study:

  • To develop a dynamic data structure for efficiently solving the membership problem for automata processing streamed input.
  • To analyze the complexity of dynamic acceptance for timed automata with interleaved symbols and time spans.
  • To provide an efficient method for online acceptance checking of timed words.

Main Methods:

  • Utilizing parameterized dynamic data structures, where automaton size is the parameter.
  • Designing a data structure that updates incrementally as each symbol of the input word is revealed.
  • Deriving complexity bounds for the dynamic acceptance problem in the context of timed automata.

Main Results:

  • A novel dynamic data structure is presented for maintaining the acceptance status of a fixed one-clock timed automaton.
  • The data structure achieves an amortized update time of O(log n) per input symbol.
  • Complexity bounds for the dynamic acceptance problem for timed automata are established.

Conclusions:

  • The developed dynamic data structure significantly improves the efficiency of online membership testing for timed automata.
  • This work bridges automata theory with dynamic data structures, offering practical solutions for streaming data analysis.
  • The findings have implications for real-time systems and verification tasks involving timed sequences.