Active Learning of Nondeterministic Finite State Machines

Algorithm 1

The algorithm 𝐿^∗_𝑁𝑀.

input: A set of input symbols 𝐼, the number of repeated queries 𝑘

output: ONFSM conjecture 𝑀

  // Construct the initial observation table (𝑆,𝐸,𝑇)

(1) set 𝑆={𝜖},𝐸=𝐼, and update 𝑇 using output queries by asking each query 𝑘 times;

(2) add 𝜖⋅𝑖/𝑜 to 𝑆⋅𝐼/𝑂 for all 𝑖∈𝐼,𝑜∈𝑇(𝜖,𝑖), and update 𝑇 using output queries by asking each query 𝑘 times;

(3)  repeat

    // Check whether the table is closed

(4)  while  found 𝑡∈𝑆⋅𝐼/𝑂 such that 𝑡≇_𝐸𝑠, for all 𝑠∈𝑆  do

(5)    move 𝑡 to 𝑆;

(6)    add 𝑡⋅𝑖/𝑜 to 𝑆⋅𝐼/𝑂 for all 𝑖∈𝐼,𝑜∈𝑇(𝑡,𝑖), and update 𝑇 using output queries by asking each query 𝑘 times;

(7)  end

(8)   make the ONFSM conjecture 𝑀 from (𝑆,𝐸,𝑇);

(9)  if  the Teacher replies with a counterexample 𝑐𝑒  then

(10)  if  any prefix of 𝑐𝑒 has been recorded in 𝑇 with a different value, then terminate with no solution;

(11)   else

(12)   find the longest 𝑢∈𝑆∪𝑆⋅𝐼/𝑂 such that 𝑐𝑒=𝑢⋅𝑣;

(13)   add the input sequence of 𝑣 and all of its suffixes to 𝐸, and update 𝑇 using output queries by asking each query 𝑘 times;

(14)   end

(15)   end

(16)  until  the Teacher replies “yes”;

(17) return the conjecture 𝑀;