Advanced Proof Viewing in ProofTool

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen's original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization which we have found out to be crucial for analyzing proofs. We then evaluate recent developments in tree visualization with regard to these criteria and propose the Sunburst Tree layout as a complement to the traditional tree structure. This layout constructs inferences as concentric circle arcs around the root inference, allowing the user to focus on the proof's structural content. Finally, we describe its integration into ProofTool and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785

VLSI Architecture and Design

Integrated circuit technology is rapidly approaching a state where feature sizes of one micron or less are tractable. Chip sizes are increasing slowly. These two developments result in considerably increased complexity in chip design. The physical characteristics of integrated circuit technology are also changing. The cost of communication will be dominating making new architectures and algorithms both feasible and desirable. A large number of processors on a single chip will be possible. The cost of communication will make designs enforcing locality superior to other types of designs. Scaling down feature sizes results in increase of the delay that wires introduce. The delay even of metal wires will become significant. Time tends to be a local property which will make the design of globally synchronous systems more difficult. Self-timed systems will eventually become a necessity. With the chip complexity measured in terms of logic devices increasing by more than an order of magnitude over the next few years the importance of efficient design methodologies and tools become crucial. Hierarchical and structured design are ways of dealing with the complexity of chip design. Structered design focuses on the information flow and enforces a high degree of regularity. Both hierarchical and structured design encourage the use of cell libraries. The geometry of the cells in such libraries should be parameterized so that for instance cells can adjust there size to neighboring cells and make the proper interconnection. Cells with this quality can be used as a basis for "Silicon Compilers"

Geometrically-constrained, parasitic-aware synthesis of analog ICs

In order to speed up the design process of analog ICs, iterations between different design stages should be avoided as much as possible. More specifically, spins between electrical and physical synthesis should be reduced for this is a very time-consuming task: if circuit performance including layout-induced degradations proves unacceptable, a re-design cycle must be entered, and electrical, physical, or both synthesis processes, would have to be repeated. It is also worth noting that if geometric optimization (e.g., area minimization) is undertaken after electrical synthesis, it may add up as another source of unexpected degradation of the circuit performance due to the impact of the geometric variables (e.g., transistor folds) on the device and the routing parasitic values. This awkward scenario is caused by the complete separation of said electrical and physical synthesis, a design practice commonly followed so far. Parasitic-aware synthesis, consisting in including parasitic estimates to the circuit netlist directly during electrical synthesis, has been proposed as solution. While most of the reported contributions either tackle parasitic-aware synthesis without paying special attention to geometric optimization or approach both issues only partially, this paper addresses the problem in a unified way. In what has been called layout-aware electrical synthesis, a simulation-based optimization algorithm explores the design space with geometric variables constrained to meet certain user-defined goals, which provides reliable estimates of layout-induced parasitics at each iteration, and, thereby, accurate evaluation of the circuit ultimate performance. This technique, demonstrated here through several design examples, requires knowing layout details beforehand; to facilitate this, procedural layout generation is used as physical synthesis approach due to its rapidness and ability to capture analog layout know-how.Ministerio de Educación y Ciencia TEC2004-0175

Satisfiability Modulo Theory based Methodology for Floorplanning in VLSI Circuits

This paper proposes a Satisfiability Modulo Theory based formulation for floorplanning in VLSI circuits. The proposed approach allows a number of fixed blocks to be placed within a layout region without overlapping and at the same time minimizing the area of the layout region. The proposed approach is extended to allow a number of fixed blocks with ability to rotate and flexible blocks (with variable width and height) to be placed within a layout without overlap. Our target in all cases is reduction in area occupied on a chip which is of vital importance in obtaining a good circuit design. Satisfiability Modulo Theory combines the problem of Boolean satisfiability with domains such as convex optimization. Satisfiability Modulo Theory provides a richer modeling language than is possible with pure Boolean SAT formulas. We have conducted our experiments on MCNC and GSRC benchmark circuits to calculate the total area occupied, amount of deadspace and the total CPU time consumed while placing the blocks without overlapping. The results obtained shows clearly that the amount of dead space or wasted space is reduced if rotation is applied to the blocks.Comment: 8 pages,5 figure