Using Structure of Automata for Faster Synchronizing Heuristics

Synchronizing Heuristics for Weakly Connected Automata with Various Topologies

“…To keep the paper self-contained, we explain the SCC method given in [1]. Consider an automaton A = (S, Σ, S×Σ, δ) and its SCC decomposition {A 1 , A 2 , …, A k }.…”

“…These automata are called as strongly connected components (SCCs) of A. In [1], given a weakly connected automaton A, a method is suggested to build a synchronizing sequence for A by using the synchronizing sequences of the SCCs of A. We will call the method suggested by [1] as the SCC method.…”

“…In [1], the SCC method has been experimented on randomly generated automata. Both Greedy and SynchroP algorithms have been applied to the strongly connected components of the automaton.…”

“…The SCC method has proven itself by improving running time greatly in both algorithms. In [1], our aim was to find if taking the SCCs into account yields a better, faster heuristic, however we lacked variety in graph generation.…”

Using Synchronizing Heuristics to Construct Homing Sequences

“…This computation is performed by using a backward breadth first search (see e.g. Figure 4 in (Cirisci et al, 2018)), rooted at s-pairs {s i , s i } ∈ S s 2 , where these s-pair nodes are the nodes at level 0 of the BFS forest. A d-pair {s i , s j } appears at level k of the BFS forest if |τ {i, j} | = k. When the automaton has a synchronizing sequence, each dpair should have a merging word since it is a necessary condition for synchronizing automata (Eppstein, 1990).…”