When hardware and software grows in size, they create a lot of pain in ass of the developers and users alike. Frankly, most of these improvement are not necessary e.g. the behemoth Microsoft Word which is good for nothing. If a console application is doing my job effectively, why would I add so much of crap known as Graphical User Interface. But there are few areas where increase in size, mostly translate into effectiveness and improvement. Hardcore VLSI is one of that area.
When one builds a large system, first thing one asks oneself, is it correct? Well first one has to write it down clearly. These written description are specification. Even if the probability of occurrence of an error in design is 1 in a million still you’ll get hundreds of them in a modern VLSI system. And any of these errors can throw you out of business. Verification and testing takes more than 60-70% of all the effort required to realise a VLSI design in practise these days. So you should make sure to hire careful and geeky people like me. And instead of wasting money on buying licenses of costly softwares, you can give me 50% of that. Its like why would you pay $1000 to hire someone with a fancy automated weapon when Zedi Knight can do the same thing with light saber in 10% of that cost. But since managers are mostly dumb, he cost becomes so high that only few new designs are coming out of industries. Industries are spineless and they have not explored the possibilities how much university can offer if they show a little bit of backbone.
Academia on the other hand, sometime solely driven by curiosity only, have produced some methods which are now hijacked by industries for their own benefits. Anyway, now we get to the core of our topic.
Simulation will not work in future! That much I am sure of. You just can not simulate all the possible combination described specification in a modern day VLSI design. Even if you have 1000 of computers at your disposal. It would be foolhardy to do so. However, simulation with formal methods may yields wonderful results. We concentrate on the formal methods here. Any improvement in these methods will be of great values for VLSI verification.
Reduced Binary decision diagrams (RBDD) and Kripke Structures are very prominent tools these days. In the past, the use of formal methods in practise seemed hopeless and hence only few crazy people stuck to those. Recently, as my professor Madhav P Desai lectures implies, industries are trying out formal verification like Z notation to document a system properties more rigorously. Model checking and theorem proving (on certain structures) are being plugged in to complement more traditional one of simulation.
Before one starts verifying, one needs to write down the specification of the system clearly. Talking in terms of states are probably the most ubiquitous these days. A state machine is formed and described in some Hardware Description Language like in my favorite VHDL then one can proceed to simulation and all. Specification need not be written in standard way. The emphasis should be on the clarity of the system.
Two well established approach to verification are model checking and theorem proving. Model checking is very fast but can handle finite states. Theorem proving can handle infinite state space. In model checking, one builds a finite model of a system and check that a desired property holds in that system. This is done by search exhaustively (and some times wisely), if it does not hold and a counterexample is produced. That is its greatest strength to able to produce and error and thus suitable for debugging. Since model is finite, it will terminate. It is mostly used in hardware and protocol verification.
Two approaches are genrally used in model checking, TEMPORAL MODEL CHECKING and ‘find and automation and compare to the specification to determine whether or not its behaviour conforms to that specification ‘. For example, Language Inclusion (Har’El and Krushan, 19941], refinement ordering [Cleaveland et all. 93], observal equivalence [Cleaveland et all 93, Fernandez, 96, Roy and de Simone 90]. Vardi and Wolper  have shown how the temporal model checking problem could be recast in terms of automata, thus relating two approaches.
Model checking is much faster than theorem proving. But the problem is STATE EXPLOSION. There are heuristics to improve this though [Krushan 1994; Krushan 1994] and semantic minimization (Elseaidy et al. 1996] to eliminate unnecessary states from a system modeling. Using this method one has verified 10^120 reachable states.
Theorem proving can deal with infinite state space. It uses structural induction to prove over infinite domains.
The overreaching goal of formal methods is to help engineers construct more reliable systems. Decomposition of a larger set into smaller sets will always be beneficial. A global property is broken into local properties which are conceptually easier to handle. Abstraction is also needed, for example, hardware specification can written down in more abstract language like esteral. Combination of mathematical theories is also a very less explored area. One solid concepts from one discipline can find application in another numerous fields, graph theory is one of the most remarkable example of it. And finally, who can forget to include better data structures and algorithms.
One can get more ambitious. rather than building models for some specific problem, one can romanticise “meta-tools” which themselves can produce or change themselves to handle a particular problem domain. Integration of available methods will also help.
 Model checking at CMU.fa