C-Y. Tsui, M. Pedram, and A. M. Despain. Exact and approximate methods for calculating signal and transition probabilities in fsms. In Proceedings of the 31st Design Automation Conference, pages 18--23, June 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....encoding program (i.e. for encoding inputs, outputs, and states) targeted for multi level implementations. This tool is included in the SIS system [6] 2. 2 Approaches for Low Power State Encoding Main works in low power FSMs compute first the switching activity and transition probabilities [7]. The key idea is the reduction of the average activity by minimizing the bit changes during state transitions. In [8] a probabilistic description of the state machines is used. Then, the state assignment minimizes the Hamming distance between states with high transition probability. To obtain ....

C-Y Tsui, M. Pedram, A.M. Despain, Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs, 3Ist Design Aut. Conf., pp. 18-23, 1994.

....Thus, the activity can be reduced. Then, these submachines must be efficiently mapped in a FPGA, so that the hardware overhead does not compensate the power saving of a lower node activity. H.a. Calculating Probabilities In order to decide the submachine partitioning, a probabilistic model [24] must be utilized. To compute the transition probabilities for a given STG, it is first necessary to know the probability distribution for the inputs. Those values can be obtained by a higher level simulation of FSM in a context close to the actual environment of the design. Then, the transition ....

C-Y Tsui, M.Pedram, A. Despain, Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs, 31st Design Autore. Conf., pp. 18-23, 1994.

....[5] Essentially this means an equation is produced for each internal input and output node that describes a relationship between the switching activity of that node and the primary inputs. In probabilistic simulation the statistical properties, as collected from analysis of the primary inputs [19], are propagated through a netlist in order to obtain the switching activity of all the nodes in that netlist. 2.2 Power estimation in asynchronous circuits There are many theories and established methodologies for the design and implementation of asynchronous circuits and systems. Some notable ....

C-Y. Tsui, M. Pedram, and A. M. Despain. Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSM's. In ACM/IEEE 31st Design Automation Conference, pages 18--23, San Diego, C. A., June 1994.

....[5] Methods for power estimation of combinational circuits based on primary input signal probability have been presented previously (e.g. 3, 7] Power estimation of sequential circuits [14] is significantly more difficult, because state line probabilities have to be taken into account. In [11, 20, 21] a static and a simulative approach is presented on the assumption that the inputs are uncorrelated. In the static procedure state line probabilities can be explicitly computed for circuits up to 15 flip flops [11] and approximately This work has been partially supported by DFG Project SFB 358 ....

Tsui,C.; Pedram,M.; Despain,A.: Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs. 31th DAC 1994, pp.18-23.

....flip flop power) Other existing techniques would then be applied to compute the power consumed in the combinational block. We will briefly survey the few recently proposed techniques for estimating the power in sequential circuits. All proposed techniques that handle sequential circuits [4 7] make the simplifying assumption that the FSM is Markov [8] so that its future is independent of its past once its present state is specified. Some of the proposed techniques compute only the probabilities (signal and transition) at the flip flop outputs, while others also compute the power. The ....

....too expensive. Another approach that also attempts a direct solution of the Chapman Kolmogorov equations is given in [5] While it is more e#cient, it remains quite expensive, so that the largest test case presented contains less than 30 flip flops. Better solutions are o#ered by the two papers [6, 7], which are based on solving a nonlinear system that gives the present state line probabilities, as follows. Given probabilities p u 1 , p um at the input lines, let a vector of present state probabilities P p.s. p x 1 . p xn ] be applied to the combinational logic block. ....

[Article contains additional citation context not shown here]

C-Y Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs," ACM/IEEE 31st Design Automation Conference, San Diego, CA, pp. 18--23, June 6--10, 1994.

....consider simultaneous switching of multiple primary inputs. Hence, activity of a node is overestimated. In [5] Ghosh et al. presented a method that deals with simultaneous switching of multiple primary inputs but neglected temporal correlation between primary inputs. In [3] Chou et al. and in [12], Tsui et al. presented exact methods to calculate signal probability and activity. The above methods can be used to accurately estimate the power dissipation of a circuit provided that the exact probability and activity of each primary input is known. However, accurate signal probability or ....

Tsui, C. Y., Pedram, M., and Despain, A. M. Exact and approximate methods for calculating signal and transition probabilities in FSMs. ACM/IEEE Design Automation Conf. (1994). pp. 18-23.

....power may be critically dependent on the specific vector sequences that occur during typical operation. Most existing techniques of power estimation consider simply the average switching activity and signal probability of the input signals and use either static probability propagation methods [3 6] or dynamic Monte Carlo simulation using randomly generated vectors [7, 8] In either case, one runs the risk of taking the circuit into parts of its state space where it does not belong, i.e. into modes of operation that are unrealistic and may never be exercised in practice. When this happens, ....

C-Y Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs," Design Automation Conf., pp. 18--23, June 6--10, 1994.

....by Stamoulis et al. 10 [53]and Tsui et al. 54] Other probabilistic approaches based on transition density [23] and on Binary Decision Diagrams (BDDs) 31] are proposed. All the above approaches are applicable only for combinational circuits. For sequential circuits various approaches [56] [59], have been proposed which assume that the future of FSM is dependent only on its present state and independent of its past state. As opposed to simulation based techniques, statistical techniques [34, 35, 36] do not require any specialized models for the components. The idea is to simulate the ....

C-Y Tsui, M. Pedram, A. M. Despain, "Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs", 31st Design Automation Conference, pp. 18-23, 1994.

....and then analyze their contribution separately. The statistical characteristics of the FSM is first lumped into the switching activity metrics (signal probabilities and transition densities) of the latch inputs by either a long time logic simulation [1] or solving a set of nonlinear equations [2, 3, 4]. Power dissipation of the combinational part can then be analyzed as mentioned above using such information. A major drawback of these approaches is that spatial and temporal correlations among latch signals are not considered. As the average power is very sensitive to signal correlations [5] ....

....1) For all test circuits, DIPE produces accurate average power estimates with reasonable amount of CPU time. 2) Usually, an independence interval of a few clock cycles is sufficient for the randomness hypothesis to be accepted with the specified significance level. This observation agrees with [4] on that a small unrolling factor of a FSM is generally enough for accurate power estimation. 3) The duration of the independence interval is determined dynamically and varies with the target circuit. Hence simulation efficiency is greatly improved by not assigning a pessimistic warm up period ....

C.-Y. Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs" 31st ACM/IEEE Design Automation Conf., San Diego, CA, pp. 18-23, 1994.

....power may be critically dependent on the specific vector sequences that occur during typical operation. Most existing techniques of power estimation consider simply the average switching activity and signal probability of the input signals and use either static probability propagation methods [3 6] or dynamic Monte Carlo simulation using randomly generated vectors [7, 8] In either case, one runs the risk of taking the circuit into parts of its state space where it does not belong, i.e. into modes of operation that are unrealistic and may never be exercised in practice. When this happens, ....

C-Y Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs," Design Automation Conf., pp. 18--23, June 6--10, 1994.

....by Stamoulis et al. 17]and Tsui et al. 6] Other probabilistic approaches based on transition density [5] and on Binary Decision Diagrams (BDDs) 18] have been proposed. All the above approaches are applicable only for combinational circuits. For sequential circuits various approaches [19] [21], have been proposed. Statistical techniques [22, 23] do not require any specialized models for components. The circuit is simulated with randomly generated input vectors until power converges to the average power. The convergence is tested statistical techniques. At the architectural level, ....

C-Y Tsui, M. Pedram, A. M. Despain, "Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs", 31st Design Automation Conference, pp. 18-23, 1994.

....into account different correlations among different circuits signals. Correlations among signals can be related temporaly (on the same signal at different times) 9] spatially (between different signals at the same time) and spatio temporal correlations (different signals at different times) [13, 21, 15]. In our circuits, the only correlations that are not taken into consideration by our Markov model are correlations between different input choices. Correlations among the input choices affect the probability of each trace. More specifically, they affect the probability of sequences of transition ....

C.-Y. Tsui, M. Pedram, and A. Despain. Exact and approximate methods for calculating signal and transition probabilities in fsms. In Proc. ACM/IEEE Design Automation Conference, pages 18--24, 1994. 19

....both these quantities, in fact the intuition suggests that a network with low switching activity on part of the inputs and outputs could be synthesized with also reduced internal switching activity. This is still an open problem, but accurate power estimation techniques such as those presented in [6] could allow combinational synthesis and library binding tools to exploit the low activity property of our state assignments. The last column of Table 1 shows the reduction in switching activity on the state lines. Note that if power dissipation in the memory elements is significantly higher than ....

C. Y. Tsui, M. Pedram and A. M. Despain. Exact and Approximate Methods for calculating signal and transition probabilities in FSMs. In Proc. of Design Automation Conf., pages 18 -- 25, June 1994.

....This, however, gets very expensive due to the exponential explosion in the number of states, even for FSMs of moderate size. One technique, given in [28] completely ignores this problem and assumes that all states (of the FSM) are equally probable, which is not true in practice. Other techniques [40 43] have been proposed that are based on the simplifying assumption that the FSM is Markov [34] so that its future is independent of its past once its present state is specified) This assumption is somewhat restrictive because it is only true when the sequence of input vectors at the FSM primary ....

....too expensive. Another approach that also attempts a direct solution of the ChapmanKolmogorov equations was given in [41] While it is more efficient, it remains quite expensive, so that the largest test case presented contains less than 30 FFs. Better solutions are offered by two recent papers [42, 43], which assume the FSM primary inputs are independent, and which are based on solving a nonlinear system that gives the present state line probabilities, as follows. Let a vector of present state signal probabilities P in = p 1 ; p 2 ; pn ] be applied to the combinational logic block and ....

[Article contains additional citation context not shown here]

C-Y Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs," ACM/IEEE 31st Design Automation Conference, pp. 18--23, June 1994.

....past once its present state is specified) If the signal and transition probabilities at the present state inputs of the FSM (i.e. the latch outputs) are known, then, with some approximation, any of the above combinational circuit techniques can be used to compute the power. Several approaches [40 43] have been proposed for sequential circuits, all of which make use of the above Markov assumption. Some of these compute only the probabilities (signal and transition) at the latch outputs, while others also compute the power. The approach in [40] solves directly for the transition probabilities ....

....expensive. Another approach that also attempts a direct solution of the Chapman Kolmogorov equations was given in [41] While it is more efficient, it remains quite expensive, so that the largest test case presented contains less than 30 latches. Better solutions are offered by two recent papers [42, 43], which are based on solving a non linear system that gives the present state line probabilities, as follows. Let a vector of input probabilities P in = p 1 ; p 2 ; p n ] be applied to the combinational logic block and let the n input signals be independent. At the outputs of the logic, ....

[Article contains additional citation context not shown here]

C-Y Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs," ACM/IEEE 31st Design Automation Conference, San Diego, CA, pp. 18--23, June 6--10, 1994.

....most practical burst mode specifications are less than 100 specified bursts and circuit sizes of less than 1K gates. Consequently, it is computationally feasible to use a more complexpower estimation procedure that is more accurate. Most synchronous switching estimation procedures (e.g. [5, 14, 8]) assume given switching probabilities on inputs that are symbolically propagated through all circuit nodes to the outputs. This methodology has low computation complexity, which is important since many synchronous circuits have more than 10K gates. However, it is not obvious how to derive signal ....

....among different circuits signals into the energy estimation procedure. Correlations among signals can be related temporally (on the same signal at different times) 2] spatially (between different signals at the same time) and spatio temporal correlations (different signals at different times) [5, 14, 8, 6]. In our circuits, the only correlations that are not taken into consideration by our Markov model are correlations between different branch decisions. Correlations among the branch decisions affect the probability of each burst list. We believe, however, that they do not affect the expected ....

C.-Y. Tsui, M. Pedram, and A. Despain. Exact and approximate methods for calculating signal and transition probabilities in FSMs. In Proc. ACM/IEEE Design Automation Conference, pages 18--24, 1994.

.... have been developed both for combinational and sequential circuits that are capable of handling temporal and (partly) spatial correlation of the input signals, various delay models, and allow the designer to take into account the toggle (spurious) power and trade off speed for accuracy [14] [20], 19] However, after the activities at all gate inputs and outputs have been computed and when it comes to estimating the power itself all techniques known to the authors (except for [18] and more recently [17] rely on these simplifying assumptions: 1. the only capacitance switched in a CMOS ....

....T ij (t) m Y n=1 P Theta xn (t 1) j n jS(t) i = m Y n=1 a n ij (t) 2.7) If the transition graph has no edge from vertex v i to v j then we put T ij = 0. To compute the exact state probabilities for the timehomogeneous process the Chapman Kolmogorov equations can be used [20]: P j = X P i T ij X P i = 1 (2.8) where the first sum is taken over all edges entering vertex v j and the second sum is taken over all vertices in the transition graph. The system of equations can be simplified if we notice that the sum of probabilities of the circuit being in states ....

[Article contains additional citation context not shown here]

C-Y. Tsui, M. Pedram, and A. M. Despain, "Exact and approximate methods for calculating signal and transition probabilities in FSMs." In: Proceedings of the 31st Design Automation Conference, pp. 18--23, June 1994.

No context found.

C-Y. Tsui, M. Pedram, and A. M. Despain. Exact and approximate methods for calculating signal and transition probabilities in fsms. In Proceedings of the 31st Design Automation Conference, pages 18--23, June 1994.

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C-Y. Tsui, M. Pedram, A. M. Despain, "Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs," ACM/IEEE DAC-31, pp. 18-23, San Diego, CA, Jun. 1994.

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C-Y. Tsui, M. Pedram, and A. M. Despain. Exact and approximate methods for calculating signal and transition probabilities in fsms. In Proceedings of the 31st Design Automation Conference, page , June 1994.

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C-Y. Tsui, M. Pedram, and A. M. Despain. Exact and approximate methods for calculating signal and transition probabilities in fsms. In Proceedings of the 31st Design AutomationConference, pages 18--23, June 1994.

No context found.

C-Y. Tsui, M. Pedram, and A. M. Despain. Exact and approximate methods for calculating signal and transition probabilities in fsms. In Proceedings of the 31th Design Automation Conference, pages 18--23, June 1994.

....simulation on the resulting circuit (which is hence treated as a combinational circuit) This method does not however capture the spatial correlations among present state lines and makes the simplistic assumption that the state probabilities are uniform. The above work is improved upon in [73] and [44] where results obtained by using the Chapman Kolmogorov equations for discrete time Markov Chains to compute the exact state probabilities of the machine are presented. The Chapman Kolmogorov method requires the solution of a linear system of equations of size 2 N , where N is the ....

....method requires the solution of a linear system of equations of size 2 N , where N is the number of flip flops in the machine. Thus, this method is limited to circuits with a small number of flip flops, since it requires the explicit consideration of each state in the circuit. The authors of [73] and [44] also describe a method for approximate switching activity estimation of sequential circuits. The basic computation step is the solution of a non linear system of equations in terms of the present state bit probabilities and signal probabilites for the combinational inputs of the FSM. The ....

C-Y. Tsui, M. Pedram, and A. M. Despain. " Exact and approximate methods for calculating signal and transition probabilities in fsms. " In Proceedings of the 31st Design Automation Conference, pages 18--23, June 1994.

....be written as: P (n) X S i 2SS(n) P (S i )P (AUX I(njS i ) 9) where AUX I(njS i ) is a Boolean function (of the primary inputs) which forces n to 1 given that the present state of the machine is S i . Equation (9) requires explicit enumeration of the states in SS(n) and is very costly. In [12], a method which employs an implicit enumeration of states using OBDDs is described. 2.3 Transition Probability Calculation The transition probability calculation can be reduced to a signal probability calculation based on equation (1) as shown in Figure 2. g is a function of PI 0 ,PI t and PS 0 ....

C. Y. Tsui, M. Pedram, and A. Despain. Exact and approximate methods for calculating signal and transition probabilities in FSMs. Technical Report CNEG 9342, Electrical Engineering-System Department, University of Southern California, October 1993. circuit Method k-unrolled with k-feedback

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C-Y Tsui, M. Pedram, A. M. Despain, "Exact and Approximate Methods for Calculating Signal and Transition Probabilities in FSMs", 31st Design Automation Conference, pp. 18-23, 1994. 79

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