Complexity of Kleene Algebra with Tests
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چکیده
Let K be a Kleene algebra with tests B. As argued in Lecture ??, the structure (Mat(n,K), ∆(n,B), +, ·, ∗, , 0n, In) again forms a Kleene algebra with tests, where Mat(n,K) denotes the family of n × n matrices over K, the operations + and · are the usual operations of matrix addition and multiplication, respectively, 0n is the n × n zero matrix, and In the n × n identity matrix. The operation ∗ on matrices is defined inductively: [ A B C D ]∗ = [ (A+BD∗C)∗ (A+BD∗C)∗BD∗ D∗C(A+BD∗C)∗ D∗ +D∗C(A+BD∗C)∗BD∗ ] (17.1)
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