The analysis of one-dimensional linear cellular automata and their aliasing properties

Abstract

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....

Design and implementation of a genetic algorithm IP core on an FPGA for path planning of mobile robots

“…Generally, there are 2 methods for implementing the random number generator [19]: linear feedback shift register (LFSR) and linear cellular automata (LCA). However, LCA generates better random numbers than LFSR does [20]. In many studies, LCA has been used for the RNGM on FPGAs [19][20][21], and hence LCA is used in this study.…”

“…However, LCA generates better random numbers than LFSR does [20]. In many studies, LCA has been used for the RNGM on FPGAs [19][20][21], and hence LCA is used in this study. The LCA consists of 16 cells, which are based on rule 90 and rule 150 as described by Wolfram [22,23] in Eqs.…”

“…Serra [20] showed that a 16-cell LCA, whose cells were updated by the rule sequence 150-90-150, produces a maximum length cycle. Figure 4 shows a hybrid LCA that uses the structure of rules 90 and 150.…”

Analysis of 90/150 CA Concatenated using Inverse Symmetric Transition Rule

“…In most simple case, a CA cell can exhibit two different states (0 or 1) and the next state of each cell depends on the present states of its three neighborhoods including itself. According to rule 90, the value of a particular cell i is the sum modulo 2 of the values of its two neighboring cells(left and right) on the previous time step t. And in rule 150, the value of a particular cell i is the sum modulo 2 of the values of its two neighboring cells and the value of cell i on the previous time step t. A natural form for the specification of 90/150 CA is an n-tuple 12 …”

“…For these reasons CA have been used for various applications such as pattern classification ( [2], [3]), cryptography ([4] ~ [8]), and pseudorandom-number generation, etc. ( [9] ~ [12]). Cho et al ([11], [13]) analyzed characteristic polynomials of group CA and non-group CA.…”