Decomposing Permutation Automata

  title={Decomposing Permutation Automata},
  author={Isma{\"e}l Jecker and Nicolas Mazzocchi and Petra Wolf},
A deterministic finite automaton (DFA) A is composite if its language L(A) can be decomposed into an intersection ⋂k i=1 L(Ai) of languages of smaller DFAs. Otherwise, A is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those… 

Figures from this paper

Multi-Parameter Analysis of Finding Minors and Subgraphs in Edge Periodic Temporal Graphs
We study the computational complexity of determining structural properties of edge periodic temporal graphs (EPGs). EPGs are time-varying graphs that compactly represent periodic behavior of


Unary Prime Languages
It is able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs.
Decomposition of safe languages
  • Amirim Research Project report from the Hebrew University
  • 2018
Finite State Machines in Hardware: Theory and Design (with VHDL and SystemVerilog)
This book describes crucial design problems that lead to incorrect or far from optimal implementation and provides examples of finite state machines developed in both VHDL and SystemVerilog (the successor of Verilog) hardware description languages.
Prime Languages
Ramanujan's Proof of Bertrand's Postulate
The revised proof of Ramanujan's proof of Bertrand's postulate is elegant and elementary so as to be accessible to a wider audience.
Reversibility of Computations in Graph-Walking Automata
It is demonstrated that every graph-walking automaton can be transformed to an equivalent reversible graph- walking automaton, so that every step of its computation is logically reversible.
Principles of model checking
Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
Apparatus and method for large hardware finite state machine with embedded equivalence classes
  • 2007
Irreversibility and heat generation in the computing process
Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.
Compositionality : the significant difference : international symposium, COMPOS '97, Bad Malente, Germany, September 8-12, 1997 : revised lectures
The Need for Compositional Proof Systems is surveyed, as well as compositional proof methods for concurrency: A semantic approach.