Hallo....i have a problem to solve regarding weigthed automata-in semirings(the automata are defined by matrices).. so i have to find the behaviour automaton through the solution of linear system..for simplicity i have constructed the follwing weigthed automaton : in the semiring of natural numbers , for an alphabet with two letters A= (a,b) I took 2 states qo and q1, qo is the initial state with initial weight 1 and q1 is the final state with final weight 1..i have the transitions from qo to q1 with weight 1 (letter a) from q1 to q1 (letters a and b)..i have proved through the definition of its behaviour that its equal to 2 but i cannot understand how to prove tis with linear systems ..i have tried to several times but my results are not equal to 2............my question is unfortunately very specific..i didnt know were to post it in the forum..i hope you can give me some instructions...thanks in advance............ :)