No abstract available.

The direct product A X B of two automata A and B has been defined by Rabit~ a~d Scott [1] while the automorphism group of A X B has been investig,~tcd by Fleck [3I The latter showed tha~ the strongly connected automaton A with a transitive abelian auto-m0rphism group G(A) is the direct product of automata if and only if G(A) is isomorphic to the direct product of two groups.The present paper considers somewhat of the reverse problem.If G and H are groups of regular permutations on the finite sets S ~rnd 7' respec~ ~ivcly, there are nonunique strongly connected automata A and B whose automorphism groups are G and H respecLively.To what extent the automorphism group of A )< H is determined by G and H is studied.A sufficient conditiotl that G X H be the group of A X H is produced and it is shown that if G and H are cyclic, there are always automata A ~md B for which G X H is the automorphism group of A X B.

article Free Access Share on The Structure of an Automaton and Its Operation-Preserving Transformation Group Author: G. P. Weeg Michigan State University, East Lansing, Michigan Michigan State University, East Lansing, MichiganView Profile Authors Info & Claims Journal of the ACMVolume 9Issue 3July 1962 pp 345–349https://doi.org/10.1145/321127.321131Published:01 July 1962Publication History 34citation380DownloadsMetricsTotal Citations34Total Downloads380Last 12 Months18Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

article Free AccessTruncation Error in the Graeffe Root-Squaring Method Author: Gerard P. Weeg Michigan State University, East Lansing, Michigan Michigan State University, East Lansing, MichiganView Profile Authors Info & Claims Journal of the ACMVolume 7Issue 1pp 69–71https://doi.org/10.1145/321008.321017Published:01 January 1960Publication History 1citation298DownloadsMetricsTotal Citations1Total Downloads298Last 12 Months16Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Decimal computers ordinarily use a binary-coded decimal representation. One class of binary-coded decimal digits is the so-called four-bit weighted code representation with weights 𝒲1𝒲2𝒲3𝒲4Iis a nonzero integer in the range -9≤𝒲I≤9, and the set of weights must have the property that every decimal digit can be represented by the sum ㎣i=14bI𝒲I, with the bIbeing 0 or 1. For some weighted codes the weights are such that some digits can be represented by more than one sum of the specified form. For example, the 7421 weighted code has the property that 7 may be represented either as 1000 or as 0111. This paper produces a necessary and sufficient condition on the weights of a weighted code for the unique representation of each digit by a sum of the specified form. Further, all possible sets of weights are displayed.