In this paper a previously proven uniqueness theorem for nonnegative cohomology theories on the same space is extended to cohomology theories on the same finite-dimensional space. In this form it is applicable to extraordinary cohomology theories. An example is given to show that the theorem does not hold without finite dimensionality.

In this paper a synthesis procedure (or self-tenable finite nalt machines is presenled. Tenability is abudy considered while transforming the behavioral description of the Muil into • struCtural description. To this end a novel state encoding algorithm as well as a modified self'lI::s! architecture are devel oped. Expc:rimentalrcsuiu show that this approach leads to a significant reduction of h...

One can construct any finite-state machine as a cascade interconnection of machines whose inputs either permute the states or reset them all to one state. Each permutation group needed in the construction is a homomorphic image of a group generated by the action of a set of input sequences on a state subset of the original machine. Proofs of these facts will be given and their application to th...

The attached figure describes the finite state machine used in TENEX version 1.33 to implement the ARPANET Host to Host protocol. This memo updates that of 27 August 1971, TENEX memo number 113, with regard to the finite state machine. Other parts of that memo have been incorporated into the JSYS manual and other documents.

(17) holds for any g in C p , and the rightmost two terms go to zero as n +m, it follows from (10) that MVJw,) + A,AT. To show that (9) converges to zero if o is not a signal frequency, it suffices to set A , = 0. Then o1 is no longer a signal frequency. In this case, (17) is bounded below by zero and above by only the rightmost two terms, both of which go the zero as n + W. This proves the the...

We have formalized deterministic finite state machines closely following the textbook [9], pp. 88–119 up to the minimization theorem. In places, we have changed the approach presented in the book as it turned out to be too specific and inconvenient. Our work also revealed several minor mistakes in the book. After defining a structure for an outputless finite state machine, we have derived the s...