Example # of # of Two-graph Size without Type 1 Sharings Type 2 Sharings Type 1 and Type 2 Sharings Nodes Edges Method Any Sharings Size Reduction (%) Size Reduction (%) Table 1: Experimental Results for Regularity Extraction Algorithm

Table 2: Experimental results for symbolic analysis technique a consequence of exploiting the regularity of symbolic expressions. Experiments also showed that structural regularity of a network can lead to significant model reductions. A limitation of the proposed method is that it is not minimal in terms of the corresponding operations. APTs can also describe reducible operations i.e. multiplication by constant 1 or addition of value 0. The limitation is due to the fact that a generic parameter of a solving function can be linked to both a non-zero parameter and to constant 0. As a consequence, models for small examples are bigger than those produced by the two-graph method. Example Reference # of nodes # of edges # of common Total # of Regularity # of re-used Total # of Regularity con. templates con.templates Factor (%) con.templates con.templates Extraction (initial) (initial) (initial) (final) cuit networks do not have a structure formed of loosely connected stages. Referring to the built decomposition tree, re-used connection templates are mainly located at the lower levels of the tree. This justifies our assumption that the regularity extraction algorithm should be guided by the connectivity information between basic blocks in the network. The decomposition technique tends to create new connection templates for the upper levels of the decomposition tree. The second part of our experimental work analyzes the size of the symbolic models generated by the proposed method. We considered four example circuits and compared the size of their symbolic models with the size of the models created by traditional methods. We also studied the impact of the two types of solving function sharings (corresponding to the two regularity types) on the size of the produced models. We did not study the execution time of the symbolic analysis technique as the models for all examples were set up in less than 1 second. The four examples are proposed by Wambacq et al [16] as workbench for comparing different symbolic methods. The reason for considering circuit networks and not system networks i.e. filters for evaluating our symbolic technique is that we intend to show its effectiveness for tightly coupled networks. Existing hierarchical symbolic methods [13] [5] were proven to be effective only for loosely coupled networks. Following four examples were used as a workbench: Network-a network of six resistors and two current sources. CMOS Miller OTA-a CMOS Miller-compensated operational transconductance amplifier (OTA), a BiCMOS Miller-compensated OTA and …