Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an Ž . equivalence class of k-ary strings under rotation the cyclic group . A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algo-Ž . rithms for generating i.e., listing all necklaces and binary unlabeled necklaces. These algorithms have optimal running times in the sense that their running times are proportional to the number of necklaces produced. The algorithm for generating necklaces can be used as the basis for efficiently generating many other equivalence classes of strings under rotation and has been applied to generating bracelets, fixed density necklaces, and chord diagrams. As another application, we describe the implementation of a fast algorithm for listing all degree n irreducible Ž . and primitive polynomials over GF 2 . ᮊ

It is shown how to construct a general linear hybrid cellular automaton (CA) such that it h cycle, and how the aliasing properties of such automata compare with linear feedback sh when used as signature analyzers. The construction is accomplished by formally demons isomorphism which binds this kind of CA to the LFSRs. Consequently, these CAs can be machines. Linear algebraic techniques are then applied appropriately for the transformat search algorithm is developed which, given an irreducible characteristic polynomial, finds linear hybrid automaton. Such CAs are tabulated for all irreducible and primitive polynom plus a selection of others of higher degree. The behavior of a linear hybrid CA and that o LFSR are similar-that is, they have the same cycle structure and only relabel the states. properties, when they are used as signature analyzers, remain unchanged Index Terms InspecControlled Indexing finite automata logic testing Non-controlled Indexing aliasing properties cycle structure irreducible characteristic polynomial isomo hybrid automaton linear machines maximum length cycle one-dimensional lin automata search algorithm signature analyzers Author Keywords Not Available References No references available on IEEE Xplore. Citing Documents 1 CA-based byte error-correcting code, Chowdhury, D.R.; Gupta, I.S.; Chaudhuri, P.P. Computers, IEEE Transactions on On page(s): 371-382, Volume: 44, Issue: 3Abstract | Full Text: PDF (952) Access this document Abstract | Full Text: PDF (772) 3 A deterministic built-in self-test generator based on cellular automata structures, Bou B. Computers, IEEE Transactions on On page(s): 805-816, Volume: 44, Issue: 6, Jun 1995 Abstract | Full Text: PDF (988) 4 Analysis of periodic and intermediate boundary 90/150 cellular automata, Nandi, S.; P Computers, IEEE Transactions on On page(s): 1-12, Volume: 45, Issue: 1, Jan 1996 Abstract | Full Text: PDF (1052) 5 BIST test pattern generators for two-pattern testing-theory and design algorithms, Ch S.K. Abstract | Full Text: PDF (948) 7 Theory and application of nongroup cellular automata for synthesis of easily testable machines, Chakraborty, S.; Roy Chowdhury, D.; Pal Chaudhuri, P. Computers, IEEE Transactions on On page(s): 769-781, Volume: 45, Issue: 7, Jul 1996 Abstract | Full Text: PDF (1240) 8 Analysis of one-dimensional linear hybrid cellular automata over GF(q), Cattell, K.; M Computers, IEEE Transactions on On page(s): 782-792, Volume: 45, Issue: 7, Jul 1996 Abstract | Full Text: PDF (896) 9 CAA decoder for cellular automata based byte error correcting code , Sasidhar, K.; C Chaudhuri, P.P. Abstract | Full Text: PDF (276) 11 On-line and off-line testing with shared resources: a new BIST approach, Xiaoling Su Abstract | Full Text: PDF (1012) 13 Cellular-automata-array-based diagnosis of board level faults, Chattopadhyay, S.; Ch Bhattacharjee, S.; Chaudhuri, P.P. Abstract | Full Text: PDF (492) 14 A unified analytical expression for aliasing error probability using single-input externa LFSR, Elsaholy, M.S.; Shaheen, S.I.; Seireg, R....

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