Vanbekbergen, P., Lin, B., Goosens, G., Man, H. D.: A generalized state assignment theory for transformations on signal transition graphs, Proc. Int. Conf. on Computer Aided Design, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by means of event insertion) to satisfy the implementability properties. It includes state assignment by solving the Complete State Coding problem [4, 5] coupled with logic minimization and speedindependent technology mapping to a target library [51, 3, 25] Related approaches can be also found in [56, 1, 30]. Methods based on the theory of state regions [12, 40, 6] provide an ecient framework for the solution of the above tasks, as they allow us to treat uniformly large sets of markings. State regions are also well suited for symbolic manipulation. These methods are discussed in Section 8. 2 Basic ....

....icts are resolved . Such an iterative procedure can be formulated as follows: 1. Partition SG states into two subsets S . The inserted signal will have value 0 in all states of set S and value 1 in all states of set S . Vanbekbergen et al. rst formulated a similar procedure in [56] but attempted to solve all con icts at once. This is suboptimal and can fail to nd a feasible solution in some cases. 36 2. Insert a new signal to switch between the states from S . For this, nd subsets of states S S and S S such that the inserted signal is enabled to re ....

Peter Vanbekbergen, Bill Lin, Gert Goossens, and Hugo de Man. A generalized state assignment theory for transformations on signal transition graphs. Journal of VLSI Signal Processing, 7(1/2):101{ 115, February 1994.

....blocks of partitioning. Each of these state signals can be inserted using excitation regions or states that immediately follow excitation regions (switching regions) References [40] and [41] improve in terms of execution time over the previous methods that claimed broader generality (e.g. [37]) by adopting a coarser granularity in the exploration of the solution space. This coarser granularity has a price, though: as we will show in Section X, there are examples of STG s which cannot be solved by their method (nor by the previous ones, mainly due to the large number of states) unless ....

....that . 2) Similar to TS transformations, both sets for insertion and must be SIP sets. In addition, consistency of state assignment for signal is required. Given an SG with a set of binary states , a partition for the insertion of signal , called an partition, is a partition of into four blocks [37]: and . defines the states in which will have the stable value 0 (1) defines . Property 6.1: Let be a consistent SG, and let be an partition of .SG obtained by inserting signal by partition is consistent iff the only allowed arcs crossing boundaries of the partition blocks are the ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man, "A generalized state assignment theory for transformations on signal transition graphs," in Proc. Int. Conf. Computer-Aided Design, Nov. 1992, pp. 112-- 117.

.... with resynthesis has beenproposed in [8, 7] The approach combines together efficient algebraic factorization techniques used in multi level combinational logic synthesis (finding candidates for decomposition) and speed independence preserving signal insertion (the latter idea originated in [17] and was implemented efficiently in [6] The main contribution of this paper is a generalisation and extension of the above basic idea so as to cover both combinational and sequential decomposition. We have 1 developed a body of theory that allows us to prune the search space when looking ....

....Event insertion is an operation on a SG which selects a subset of states, splits each of them into two states and creates, on the basis of these new states, an excitation region for a new event. Figure 3 shows the chosen insertion scheme, analogous to that used by most authors in the area [17]. ER(x) a) d c b a (b) ER(x) d x c b x c x b x x a Figure 3: Event insertion scheme: a) before insertion, b) after insertion State signal insertion must preserve the speedindependence of the original specification. An inserted signal is denoted by x in this paper. The ....

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P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proceedings of the International Conference on Computer-Aided Design, pages 112--117, November 1992.

....r Gamma EB(r) Symmetrically, input borders can be handled. Figure 8 illustrates the notions of exit and input borders. Note that we need each new signal x to orderly cycle through states in which it has value 0, 0 , 1 and 1 . We can formalize this requirement with the notion of I partition ([36] used a similar definition) An I partition divides a set of all states of a TS into four blocks: S 0 , S 1 , S and S Gamma . S 0 (S 1 ) defines the states in which x will have the value 0 (1) S (S Gamma ) defines GER(x ) GER(x Gamma) For a consistent encoding of x, the ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proceedings of the InternationalConference on Computer-Aided Design, pages 112--117, November 1992.

....values in such a way that for any state change due to the firing of a transition, the signal change associated with the transition exactly corresponds to the difference between the two combinations of signal values that the two states are assigned. This is called a consistent state assignment [5]. Moreover, in order to be functionally implementable, a STG has to satisfy the complete state coding (CSC) requirement [2, 5] i.e. the set of non input signal transitions that are enabled in a state s must be completely determined by the binary code of s in a consistent state assignment. This ....

....transition exactly corresponds to the difference between the two combinations of signal values that the two states are assigned. This is called a consistent state assignment [5] Moreover, in order to be functionally implementable, a STG has to satisfy the complete state coding (CSC) requirement [2, 5], i.e. the set of non input signal transitions that are enabled in a state s must be completely determined by the binary code of s in a consistent state assignment. This condition is satisfied in particular if the STG admits a one to one consistent state assignment, where distinct states are ....

[Article contains additional citation context not shown here]

P. Vanbekbergen et al. "A Generalized State Assignment Theory for Transformations on Signal Transition Graphs", Proc. International Conf. on Computer-Aided-Design ICCAD, pp. 112-117, 1992.

....to avoid hazards. This is achieved in two major steps: 1) finding a logic decomposition of the complex gate circuit based on algebraic factorization originally proposed for combinational logic [19] 2) inserting new signals whilst preserving overall hazard freedom, based on an idea proposed in [20] and on the efficient implementation techniques described in [21] Both these parts are provided with an appropriate progress condition check and cost function evaluation, so as to achieve global optimization. The method has been embedded into the overall synthesis procedure implemented in the ....

....conflicts. Fig. 5 depicts a new SG in which a new signal, csc0, has been inserted. Now the next state functions for signals LDS and can be uniquely defined. The insertion of new signals must be done in such a way that the resulting SG satisfies consistency and speed independence, as discussed in [20] and [21] 3) Next State Function Implementation: Once the nextstate function has been derived, Boolean minimization can be performed to obtain a logic equation that implements the behavior of the signal. In this step it is crucial to make an efficient use of the don t care conditions. For the ....

[Article contains additional citation context not shown here]

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man, "A generalized state assignment theory for transformations on signal transition graphs," in Proc. Int. Conf. Computer-Aided Design, Nov. 1992, pp. 112--117.

....by means of event insertion) to satisfy the implementability properties. It includes state assignment by solving the Complete State Coding problem [4, 5] coupled with logic minimization and speedindependent technology mapping to a target library [51, 3, 25] Related approaches can be also found in [56, 1, 30]. Methods based on the theory of state regions [12, 40, 6] provide an efficient framework for the solution of the above tasks, as they allow us to treat uniformly large sets of markings. State regions are also well suited for symbolic manipulation. These methods are discussed in Section 8. 2 ....

....19 . Such an iterative procedure can be formulated as follows: 1. Partition SG states into two subsets S 0 and S 1 . The inserted signal will have value 0 in all states of set S 0 and value 1 in all states of set S 1 . 19 Vanbekbergen et al. first formulated a similar procedure in [56] but attempted to solve all conflicts at once. This is suboptimal and can fail to find a feasible solution in some cases. 36 2. Insert a new signal to switch between the states from S 0 and S 1 . For this, find subsets of states S ae S 0 and S Gamma ae S 1 such that the inserted ....

Peter Vanbekbergen, Bill Lin, Gert Goossens, and Hugo de Man. A generalized state assignment theory for transformations on signal transition graphs. Journal of VLSI Signal Processing, 7(1/2):101-- 115, February 1994.

....level. Event insertion is an operation on an SG which selects a subset of states, splits each of them into two states and creates, on the basis of these new states, an excitation region for a new event. Fig. 3 shows the chosen insertion scheme, analogous to that used by most authors in the area [19]. We shall say that an inserted signal is acknowledged by a signal ,if is one of the signals delayed by the insertion of . The same terminology will be used for the corresponding transitions. For example, acknowledges in Fig. 3. State signal insertion must preserve the speed independence of the ....

....with the so called state diamonds of SG [5] These conditions are illustrated by Fig. 4, where all possible cases of illegal intersections of with state diamonds are shown. The first (rather inefficient) method for finding SIP sets based on a reduction to the satisfiability problem was proposed in [19]. An efficient method based on the theory of regions has been described in [5] Assume that the set of states in an SG is partitioned into two subsets which are to be encoded by means of an additional signal. This new signal can be added in order to either satisfy the CSC condition, or to break ....

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P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man,"A generalized state assignment theory for transformations on Signal Transition Graphs," in Proc. Int. Conf. Computer-Aided Design, Nov. 1992, pp. 112--117.

....level. Event insertion is an operation on an SG which selects a subset of states, splits each of them into two states and creates, on the basis of these new states, an excitation region for a new event. Figure 3 shows the chosen insertion scheme, analogous to that used by most authors in the area [19]. We shall say that an inserted signal a is acknowledged by a signal b, if b is one of the signals delayed by the insertion of a, the same terminology will be used for the corresponding transitions) For example, d acknowledges x in Figure 3. State signal insertion must preserve the ....

....r with the so called state diamonds of SG [5] These conditions are illustrated by Figure 4, where all possible cases of illegal intersections of r with state diamonds are shown. The rst (rather inecient) method for nding SIP sets based on a reduction to the satis ability problem was proposed in [19]. An ecient method based on the theory of regions has been described in [5] Assume that the set of states S in an SG is partitioned into two subsets which are to be encoded by means of an additional signal. This new signal can be added in order to either satisfy the CSC condition, or to break up ....

[Article contains additional citation context not shown here]

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proceedings of the International Conference on Computer-Aided Design, pages 112-117, November 1992.

....has been also used for the same purpose. Table 1 summarizes the most significant efforts in the area of CSC for Petri nets. Among the different subclasses of Petri nets, algorithms have been proposed for Marked Graphs (MGs) Van90, KKT91] Free Choice nets [LMBSV92] and general Petri nets [VLGM92]. A common characteristic of these techniques is that the State Graph (SG) derived from the net is the main data structure used to analyze the CSC property (excepting [Van90] for MGs) Since the size of the SG can be exponential depending on the number of signals of the circuit, algorithms using ....

....state signals to disambiguate potential USC conflicts. The reason why we use USC instead of CSC is that CSC requires a more exhaustive analysis of the STG that would make the algorithm 1 MG FC net Petri net time [Van90] Theta O(n 4 ) KKT91] Theta exponent. LMBSV92] Theta Theta exponent. [VLGM92] Theta Theta Theta exponent. This paper Theta Theta O(n 4 ) Table 1: Previous techniques for CSC of Petri nets exponential. In spite of using a more restrictive property, we have found that our algorithm yields to better results that those obtained by existing exponential time techniques. ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on signal transition graphs. In Proc. of the Int. Conf. on Computer-Aided Design, pages 184--187, November 1992. 19

....values in such a way that for any state change due to the firing of a transition, the signal change associated with the transition exactly corresponds to the difference between the two combinations of signal values that the two states are assigned. This is called a consistent state assignment [5]. Page 5 Moreover, in order to be functionally implementable, a STG has to satisfy the complete state coding (CSC) requirement [2, 5] i.e. the set of non input signal transitions that are enabled in a state s must be completely determined by the binary code of s in a consistent state ....

....exactly corresponds to the difference between the two combinations of signal values that the two states are assigned. This is called a consistent state assignment [5] Page 5 Moreover, in order to be functionally implementable, a STG has to satisfy the complete state coding (CSC) requirement [2, 5], i.e. the set of non input signal transitions that are enabled in a state s must be completely determined by the binary code of s in a consistent state assignment. This condition is satisfied in particular if the STG admits a one to one consistent state assignment, where distinct states are ....

[Article contains additional citation context not shown here]

P. Vanbekbergen et al. "A Generalized State Assignment Theory for Transformations on Signal Transition Graphs", Proc. International Conf. on Computer-Aided-Design ICCAD, pp. 112-117, 1992.

....the notions of exit and input borders. 10 a a r b c d Input border Exit border Figure 8: Exit and input borders Note that we need each new signal x to orderly cycle through states in which it has value 0, 0 , 1 and 1 . We can formalize this requirement with the notion of I partition ([36] used a similar definition) An I partition divides a set of all states of a TS into four blocks: S 0 , S 1 , S and S Gamma . S 0 (S 1 ) defines the states in which x will have the value 0 (1) S (S Gamma ) defines GER(x ) GER(x Gamma) For a consistent encoding of x, the ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proceedings of the International Conference on ComputerAided Design, pages 112--117, November 1992. 15

....the notions of exit and input borders. a a r b c d Input border Exit border Figure 8: Exit and input borders Note that we need each new signal x to orderly cycle through states in which it has value 0, 0 , 1 and 1 . We can formalize this requirement with the notion of I partition ([37] used a similar definition) An I partition divides a set of all states of a TS into four blocks: S 0 , S 1 , S and S Gamma . S 0 (S 1 ) defines the states in which x will have the value 0 (1) S (S Gamma ) defines GER(x ) GER(x Gamma) For a consistent encoding of x, the ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proceedings of the International Conference on ComputerAided Design, pages 112--117, November 1992. 15

....language generated by the STG. The latter implies that the implementability conditions (determinism, commutativity, persistency, deadlock freedom and consistency) must be preserved in the transformed specification. Related Work. A number of methods for solving the CSC problem are known to date [6, 8, 9, 10, 13, 14, 15, 18, 22, 23, 24, 26, 27, 30]. Reported experimental results and our own experience with the available tools for solving CSC ensured the authors of this paper that none of the published methods appears to be successful when applied to general SGs or STGs with more than a few thousand states. Methods from [13, 15, 18, 22, 24, ....

....by mapping an initial SG into a flow table synthesis problem and then using classical flow table minimization and state assignment methods. This method is restricted with live and safe free choice STGs and cannot process large SGs due to limitations of classical state assignment methods. In [23, 26] a very general framework for state assignment is presented. The CSC problem is formulated as state variable assignment on the state graph. The correctness conditions for such assignment are formulated as a set of Boolean constraints. The solution can be found using a Boolean satisfiability ....

[Article contains additional citation context not shown here]

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. Journal of VLSI Signal Processing, 7(1-2):101--116, 1994.

....both sets for insertion, GER(x ) and GER(x Gamma) must be SIPsets. In addition, consistency of state assignment for signal x is required. Given an SG with a set of binary states S, a partition for the insertion of signal x, called I partition, is a partition of S into four blocks ([25]) S 0 , S 1 , S and S Gamma . S 0 (S 1 ) defines the states in which x will have the stable value 0 (1) S (S Gamma ) defines GER(x ) GER(x Gamma) Let A be a consistent SG and let I = fS 0 ; S 1 ; S S Gamma g be an I partition of A. SG A 0 obtained by ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proceedings of the International Conference on ComputerAided Design, pages 112--117, November 1992.

....behaves as assumed by the operation mode. Furthermore, this implementation can be transformed into a multi level logic circuit with more restrictive delay models by using existing techniques [LMBSV92] 1. 1 Previous Work Methods for solving the CSC problem in STGs have been proposed in [Van90, LMBSV92, VLGM92, YCLGM93]. Vanbekbergen [Van90] and Ykman [YCLGM93] have presented algorithms that work directly on the STG, but only in [Van90] a polynomial time technique based on the lock graph theory has been proposed. However, this technique is only applicable to marked graphs with single transitions. The other ....

....implementation which is hazard free under the Multiple Signal Change condition. 4 A Polynomial Algorithm to Solve the CSC Problem As shown before, the analysis of the CSC property can be done at the SG level. Most algorithms proposed so far to solve the state assignment problem operate on the SG [LMBSV92, VLGM92]. Previous works based on lock relations [YCLGM93, LL92] operate directly on the STG. However, the approach presented in [YCLGM93] is restricted to marked graphs and shows an exponential worst case complexity. LL92] can be applied to FC STGs but also has an exponential worst case. Next we present ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on signal transition graphs. In Proc. of the Int. Conf. on Computer-Aided Design, pages 112--117, November 1992.

....design. The method has been automated and applied to a number of examples. 1 Introduction Asynchronous design styles are becoming increasingly popular because they offer the potential benefits of improved system performance, avoidance of clocking problems, low power operation, and modular design [8, 17, 18, 14, 26, 19, 21, 28, 2, 12, 15, 6, 27, 1]. However, the design of correct asynchronous circuitry is a difficult task since an asynchronous circuit can malfunction (i.e. produce unexpected behavior) during execution if it is not free of hazards, which correspond to undesired glitches in a circuit. This is in contrast with synchronous ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. A generalized state assignment theory for transformations on signal transition graphs. In ICCAD-1992.

.... while the latter may drive it again into meta stability while the previous meta stability has not been resolved yet, which only adds to the length of a potentially unbounded process 3 This first STG does not have CSC, so state signal transitions must be added to it to make it implementable [11, 5]. One possible solution, with one state signal s, is shown in Figure 10. a) Redundant places (i.e. places whose removal does not affect the enabling firing conditions of the net) have been removed, for the sake of clarity. We can now expand the symbolic actions wait and signal to full ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. D. Man. A generalized state assignment theory for transformations on Signal Transition Graphs. In Proc. of the Int. Conf. on Computer-Aided Design, pages 112--117, Nov. 1992.

....shown that the necessary and sufficient condition for a hazard free implementation is precisely characterized by the CSC requirement. A state graph satisfying the CSC requirement may also be implemented in a hazard free manner using only basic gates by employing the methods described in [5, 1] In [8], a generalized state assignment method was proposed for transformations at the state graph level. This method has the capability of adding new state signal transitions in a concurrent way. For example in Figure 1(a) the CSC violation can be corrected by adding a new state signal C , as shown in ....

....that transforms the state graph by removal of states. Correctness conditions are formulated as Boolean constraints. This approach can be combined with the generalized state assignment method in a compositional way by solving both the concurrency reduction and state assignment constraints [8] together in a satisfiability framework. 2 State Graph Specification 2.1 State graphs A state graph is a finite automaton given by G = hA;S; T; ffi; soi, where the components are defined as follows. A = I [ O is the set of signals, I is the set of input signals, and O is the set of non input ....

[Article contains additional citation context not shown here]

P. Vanbekbergen, B. Lin, G. Goossens, and H. de Man. A generalized state assignment theory for transformations on signal transition graphs. In Proc. of the ICCAD, pp. 112--117, Nov. 1992.

....state graph level and are consistent with the interleave firing semantics of Petri nets. This means that the proposed generalized STG model can be mapped to a finite state graph consistently and in a well defined way. Once translated to the state graph level, the synthesis procedures proposed in [6] and [7] can be used to solve the state assignment problem necessary for race free realizations. This is an important contribution which makes STGs applicable for the specification and synthesis of industrial applications (e.g. the I 2 C interface[1] instead of rather academic examples [ In ....

....Section 5. How an extended state graph is derived from a generalized STG is described in Section 6. Since the semantics of the extensions are defined at state graph level, it means that synthesis methods that work purely at the state graph level can be used. The generalized state assignment method [6] is such a method. In Section 7, a case study will be presented. Finally, concluding remarks will be given in Section 9. 2 Classical Signal Transition Graph Model. Signal Transition Graphs (STG) are used to specify the behavior of asynchronous digital control circuits. The vertices of such a ....

[Article contains additional citation context not shown here]

P. Vanbekbergen, B. Lin, G. Goossens, and H. De Man. "A Generalized State Assignment Theory for Transformations on Signal Transition Graphs.". In Proc. Int'l. Conf. Computer-Aided Design, pages 112 -- 117, 1992.

....12] has been proven to be an attractive model for the specification and synthesis of asynchronous controllers. Because it is based on Petri nets [7] it is very well suited to model concurrency and conditional behavior. Several synthesis techniques starting from the STG model have been developed [3, 4, 12, 11]. The classical STG model is intended for controllers in selftimed systems (also called self timed controllers) In selftimed systems all system events occur in a particular sequence, but nothing ever has to occur at a particular time. In most interface applications the controllers do not follow ....

P. Vanbekbergen, B. Lin, G. Goossens, and H. de Man. A generalized state assignment theory for transformations on signal transition graphs. In Proc. of the ICCAD, pp. 112--117, Nov. 1992.

....also guarantees the satisfaction of the CSC requirement. Formalizing the problem in this way makes it possible to define algorithmic synthesis procedures for transforming the initial state graph to satisfy this property, using for example, the generalized state assignment method described in [11]. The preliminary discussion of MC theory was given in [6] The remainder of this paper is organized as follows. Section II defines the state graph specification model and the basic objects that we need for the exposition of this work. Section III Permission to copy without fee all or part of ....

....to be persistent. V SYNTHESIS PROCEDURE A Outline of Synthesis One possible synthesis approach is to transform an initial state graph G to a new state graph G 0 that satisfies the MC requirement. We have worked out an approach based on the generalized state assignment framework described in [11]. This work will be described elsewhere, in a forthcoming report. The basic idea is to transform G into G 0 by encoding each state with new state variables that can take on each one of four possible values: f0; 1; up; downg. Given a particular assignment, a new state graph G 0 can be derived ....

[Article contains additional citation context not shown here]

P. Vanbekbergen, B. Lin, G. Goossens, and H. D. Man. A generalized state assignment theory for transformations on signal transition graphs. In Proc. of the ICCAD, pp. 112--117, Nov. 1992.

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Vanbekbergen, P., Lin, B., Goosens, G., Man, H. D.: A generalized state assignment theory for transformations on signal transition graphs, Proc. Int. Conf. on Computer Aided Design, 1992.

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P. Vanbekbergen, B. Lin, G. Goosens, and H. De Man. A generalized state assignment theory for transformations on signal transition graphs. Proc. of the Int. Conf. on Computer Aided Design, 184-187, 1992.

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P. Vanbekbergen, B. Lin, G. Goosens, and H. De Man. A generalized state assignment theory for transformations on signal transition graphs. Proc. of the Int. Conf. on Computer Aided Design, 184-187, 1992.

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