crystal reports upc-a barcode WORKING WITH SY MBOLIC REPRES ENTATIONS in Font

Print PDF-417 2d barcode in Font WORKING WITH SY MBOLIC REPRES ENTATIONS

CHAPTER 12 WORKING WITH SY MBOLIC REPRES ENTATIONS
Make PDF417 In None
Using Barcode generator for Font Control to generate, create PDF417 image in Font applications.
www.OnBarcode.com
Make Data Matrix 2d Barcode In None
Using Barcode drawer for Font Control to generate, create Data Matrix 2d barcode image in Font applications.
www.OnBarcode.com
// Publish the construction functions that make BDDs from existing BDDs member g.False = Bdd falseIdx member g.And(Bdd m1,Bdd m2) = Bdd(mkAnd(m1,m2)) member g.Not(Bdd m) = Bdd(-m) member g.Var(nm) = Bdd(mkNode(nm,trueIdx,falseIdx)) member g.NodeCount = nextIdx The types of these functions are as follows: val memoize : ('a -> 'b) -> ('a -> 'b) type BddIndex = int type Bdd = Bdd of BddIndex type BddNode = Node of Var * BddIndex * BddIndex type BddBuilder = class end with new : order:(Var -> Var -> int) -> BddBuilder member And : _arg1:Bdd * _arg2:Bdd -> Bdd member Not : _arg3:Bdd -> Bdd member Var : nm:Var -> Bdd member False : Bdd member NodeCount : int end Besides the functions that ensure that nodes are unique, the only substantial function in the implementation is mkAnd. This relies on the following logical rules for constructing BDD nodes formed by taking the conjunction of existing nodes. Note how the second rule is used to interleave variables. (x => P | Q) AND (x => R | S) is identical to (x => P AND R | Q AND S). (x => P | Q) AND (y => R | S) is identical to (x => P AND T | Q AND T) where T is simply (y => R | S). One final important optimization in the implementation is to memoize the application of the mkAnd operation. Given the previous implementation of BDDs, you can now add the members ToString to convert BDDs to strings, Build to convert a Prop representation of a formula into a BDD, and Equiv to check for equivalence between two BDDs: member g.ToString(Bdd idx) = let rec fmt depth idx = if depth > 3 then "..." else let (Node(p,l,r)) = idxToNode(idx) if p = "" then if l = trueIdx then "T" else "F" else sprintf "(%s => %s | %s)" p (fmt (depth+1) l) (fmt (depth+1) r) fmt 1 idx
Painting Universal Product Code Version A In None
Using Barcode encoder for Font Control to generate, create GS1 - 12 image in Font applications.
www.OnBarcode.com
PDF417 Generator In None
Using Barcode generation for Font Control to generate, create PDF-417 2d barcode image in Font applications.
www.OnBarcode.com
CHAPTER 12 WORKING WITH S YMBOLIC REPRES ENTATIONS
Make Code 128 Code Set A In None
Using Barcode creation for Font Control to generate, create ANSI/AIM Code 128 image in Font applications.
www.OnBarcode.com
Barcode Creation In None
Using Barcode generator for Font Control to generate, create Barcode image in Font applications.
www.OnBarcode.com
member g.Build(f) = match f with | And(x,y) -> g.And(g.Build x, g.Build y) | Var(p) -> g.Var(p) | Not(x) -> g.Not(g.Build x) | False -> g.False | Exists(v,p) -> failwith "Exists node" member g.Equiv p1 p2 = (g.Build(p1) = g.Build(p2)) You can now install a pretty-printer and inspect the BDDs for some simple formulae: > let bddBuilder = BddBuilder(compare);; val bddBuilder: BddBuilder > fsi.AddPrinter(fun bdd -> bddBuilder.ToString(bdd));; val it: unit = () > bddBuilder.Build(var "x");; val it : Bdd = (x => T | F) > bddBuilder.Build(var "x" &&& var "x");; val it : Bdd = (x => T | F) > bddBuilder.Build(var "x") = bddBuilder.Build(var "x" &&& var "x");; val it : bool = true > (var "x") = (var "x" &&& var "x");; val it : bool = false > bddBuilder.Build(var "x" &&& var "y");; val it : Bdd = (x => (y => T | F) | F) > bddBuilder.Equiv (var "x") (var "x" &&& var "x");; val it : bool = true Note that the BDD representations of x and x AND x are identical, while the Prop representations are not. The Prop representation is an abstract syntax representation, while the BDD representation is more of a semantic or computational representation. The BDD representation incorporates all the logic necessary to prove propositional formula equivalent; in other words, this logic is built into the representation itself.
QR Code JIS X 0510 Creator In None
Using Barcode drawer for Font Control to generate, create QR Code JIS X 0510 image in Font applications.
www.OnBarcode.com
Paint ANSI/AIM I-2/5 In None
Using Barcode printer for Font Control to generate, create Uniform Symbology Specification ITF image in Font applications.
www.OnBarcode.com
Circuit Verification with BDDs
Generating PDF 417 In None
Using Barcode printer for Online Control to generate, create PDF 417 image in Online applications.
www.OnBarcode.com
PDF-417 2d Barcode Reader In Java
Using Barcode reader for Java Control to read, scan read, scan image in Java applications.
www.OnBarcode.com
You can now use BDDs to perform circuit verification. For example, the following verifies that you can swap the x and y inputs to an 8-bit adder:
Code-39 Encoder In Java
Using Barcode drawer for Java Control to generate, create Code 39 image in Java applications.
www.OnBarcode.com
EAN 128 Creator In Objective-C
Using Barcode drawer for iPad Control to generate, create UCC-128 image in iPad applications.
www.OnBarcode.com
CHAPTER 12 WORKING WITH SY MBOLIC REPRES ENTATIONS
QR Code JIS X 0510 Encoder In Java
Using Barcode generator for Android Control to generate, create Denso QR Bar Code image in Android applications.
www.OnBarcode.com
Create Data Matrix 2d Barcode In Java
Using Barcode creation for Android Control to generate, create ECC200 image in Android applications.
www.OnBarcode.com
> bddBuilder.Equiv (nBitCarryRippleAdder 8 (vec 8 "x") (vec 8 "y") (vec 8 "sum") (vec 9 "carry")) (nBitCarryRippleAdder 8 (vec 8 "y") (vec 8 "x") (vec 8 "sum") (vec 9 "carry"));; val it : bool = true Thirty-three variables are involved in this circuit. A naive exploration of this space would involve searching a truth table of more than eight billion entries. The BDD implementation takes moments on any modern computer. Efficient symbolic representations pay off! A more substantial verification problem involves checking the equivalence of circuits that have substantial structural differences. To explore this, let s take a different implementation of addition called a carry select adder. This avoids a major problem with ripple adders caused by the fact that the carry signal must propagate along the entire length of the chain of internal adders, causing longer delays in the electrical signals and thus reducing the clock rates of a circuit or possibly increasing power consumption. A carry select adder gets around this through a common hardware trick of speculative execution. It divides the inputs into blocks and adds each block twice, once assuming the carry is low and once assuming it is high. The result is then selected after the circuit, when the carry for the block has been computed. Listing 12-16 shows the specification of the essence of the hardware layout of a carry select adder using the techniques we ve developed so far. The specification uses the slicing syntax for arrays described in 4. Listing 12-16. A Carry Select Adder Modeled Using Propositional Logic let mux a b c = ((~~~a ==> b) &&& (a ==> c)) let carrySelectAdder totalSize maxBlockSize (x:bitvec) (y:bitvec) (sumLo:bitvec) (sumHi:bitvec) (carryLo:bitvec) (carryHi:bitvec) (sum:bitvec) (carry:bitvec) = Blocks [ for i in 0..maxBlockSize..totalSize-1 -> let sz = min (totalSize-i) maxBlockSize let j = i+sz-1 let carryLo = Array.append [| False |] carryLo.[i+1..j+1] let adderLo = rippleAdder sz x.[i..j] y.[i..j] sumLo.[i..j] carryLo let carryHi = Array.append [| True |] carryHi.[i+1..j+1] let adderHi = rippleAdder sz x.[i..j] y.[i..j] sumHi.[i..j] carryHi let carrySelect = (carry.[j+1] === mux carry.[i] carryLo.[sz] carryHi.[sz]) let sumSelect = Blocks [for k in i..j -> sum.[k] === mux carry.[i] sumLo.[k] sumHi.[k]] adderLo &&& adderHi &&& carrySelect &&& sumSelect ]
GTIN - 12 Creator In Java
Using Barcode maker for Android Control to generate, create UPC-A image in Android applications.
www.OnBarcode.com
Read EAN 13 In .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in VS .NET applications.
www.OnBarcode.com
Draw Barcode In Objective-C
Using Barcode generation for iPhone Control to generate, create Barcode image in iPhone applications.
www.OnBarcode.com
Generating EAN 13 In Objective-C
Using Barcode generation for iPhone Control to generate, create EAN 13 image in iPhone applications.
www.OnBarcode.com
Paint PDF 417 In Visual C#.NET
Using Barcode printer for Visual Studio .NET Control to generate, create PDF-417 2d barcode image in Visual Studio .NET applications.
www.OnBarcode.com
ECC200 Decoder In .NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications.
www.OnBarcode.com
Copyright © OnBarcode.com . All rights reserved.