From Post Systems to the Reachability Problems for Matrix Semigroups and Multicounter Automata
The main result of this paper is the reduction of PCP(n) to the vector reachability problem for a matrix semigroup generated by n 4 × 4 integral matrices. It follows that the vector reachability problem is undecidable for a semigroup generated by 7 integral matrices of dimension 4. The question whether the vector reachability problem is decidable for n = 2 and n = 3 remains open. Also we show that proposed technique can be applied to Post’s tag-systems. As a result we define new classes of counter automata that lie on the border between decidability and undecidability.
KeywordsMembership Problem Reachability Problem Counter Machine Binary Word Pushdown Automaton
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