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Now that you have modeled the initial hardware circuits, you can check simple properties of these circuits. For example, you can check that if you give a fullAdder all low (that is, false) inputs, then the output wires may be low as well and, conversely, that you have a contradiction if one of the output wires is high: > tautology (fullAdder Lo Lo Lo Lo Lo);; val it : bool = true > satisfiable (fullAdder Lo Lo Lo Hi Lo);; val it : bool = false It is of course much better to check these results symbolically by giving symbolic inputs. For example, you can check that if the same value is given to the two inputs of a halfAdder, then the sum output is low and the carry output is the same as the input: > tautology (halfAdder (var "x") (var "x") Lo (var "x"));; val it : bool = true Likewise, you can check that a 2-bit adder is commutative, in other words, that it doesn t matter if you swap the x and y inputs. > tautology (nBitCarryRippleAdder 2 (vec 2 "x") (vec 2 "y") (vec 2 "sum") (vec 3 "carry") === nBitCarryRippleAdder 2 (vec 2 "y") (vec 2 "x") (vec 2 "sum") (vec 3 "carry"));; val it : bool = true However, if you repeat the same for sizes of 5 or bigger, things start to slow down a little, and the naive implementation of propositional logic tautology checking based on truth tables begins to break down. Hence, you have to turn to more efficient techniques for processing propositional formulae.

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This provides a way to treat the nested table contents as any relational table contents when writing queries (which should make you wonder why, instead of using a relational child table, you would ever use nested table in the first place). Notice that we don t have to give a where clause to join the two tables; Oracle internally does that for us. Alternatively, we could also use the hint nested_table_get_refs to get the same results as follows: benchmark@ORA10G> select /*+ nested_table_get_refs */ part_id, part_name, part_desc 2 from parts_nt; PART_ID ---------1 2 PART_NA ------part1 part2 PART_DESC -------------------part1 description part2 description

In practice, propositional formulae to describe hardware can be enormous, involving hundreds of thousands of nodes As a result, hardware companies have an interest in smart algorithms to process these formulae and check them for correctness The circuits in the computers you use from day to day have almost certainly been verified using advanced propositional logic techniques, often using a functional language as the means to drive and control the analysis of the circuits A major advance in the application of symbolic techniques to hardware design occurred in the late 1980s with the discovery of binary decision diagrams, a representation for propositional logic formulae that is compact for many common circuit designs BDDs represent a propositional formula via the use of if .. then .. else conditionals alone, which you write as (variable => true-branch | false-branch).

Let s look at some more DML examples. The first one inserts into the components_nt table with a select from the same table. This example is similar to the earlier example presented during the varrays discussion. Here again, the multiset keyword is used to specify that the subquery inside can return one row (without it, Oracle will give an error if the subquery returns more than one row). Similarly, the cast keyword casts a value from one type to another; we use it here to cast the resulting query value to our nested table type. Note that we use the hint nested_table_get_refs to unnest the nested table data in the inner select. Once again, the code is complicated for what would be a simple SQL statement in the case of a relational approach: benchmark@ORA10G> insert into components_nt 2 select 2, 'component 2', 3 cast 4 ( 5 multiset 6 ( 7 select /*+ nested_table_get_refs */ 2,3, part_name, part_desc 8 from parts_nt 9 where component_id = 1 10 ) as part_type_tab 11 ) 12 from components_nt c 13 where c.component_id = 1; 1 row created.