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A System to Generate Test Data and Symbolically Execute Programs Lori A. Clarke September 1976

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Existing Approach Programmer manually generates test data and tests until satisfied that program is correct Proposed alternative methods: Program correctness: formal mathematical proofs used to prove a program is correct Program validation: encompasses wide range of automated tools that analyze and evaluate programs

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Existing Approach - Problems Success depends on programmer's expertise and system complexity What criteria do we use to generate tests? Approach inadequate and costly Program correctness: Frequent human intervention required Complex and tedious, infeasible for large systems Program validation Aids in testing, but does not guarantee program is correct

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Goals of Proposed System Generate test data that drives execution down a specific path – tester specifies which path Detect non-executable program paths Create a symbolic representation of the program's output variables Detect certain types of program errors

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System Overview

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System Phases

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Phase 1: Preprocessor Uses DAVE (Osterweil and Fosdick), without its sophisticated features

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Control Flow Graph

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Control Path One way of “going” from one point to another – a path that the Control could take There could be several

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Execution Path A control path that can be executed

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Phase 2: Symbolic Execution

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Path Selection Two methods: Static – designed to accept automatically generated paths Interactive – designed to aid a human user in selecting a path

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Symbolic Execution Example Expressions, not values, are assigned. Input Fragment: READ(UNIT) B, C, D A = B + C * D C = A * 3 + 5 WRITE C How is it done? B = I1, C = I2, D = I3 A = I1 + I2 * I3 C = ( (I1+I2)*I3 )*3+5 Symbolic Outputs

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Why Symbolic Execution? Creates a human-readable symbolic representation Facilitates error-detection Aids in assertion generation Produces path constraints used in test generation

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Finding Constraints with Symbolic Execution J = I1, K = I2 J becomes I1 + 1 For control to go through path 1-5, 7, 9: I1 + 1 <= I2 [J becomes I2-(I1+1)] I2-(I1+1) > -1

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Finding Constraints with Symbolic Execution J = I1, K = I2 J becomes I1 + 1 For control to go through path 1-5, 7, 9: I1 + 1 <= I2 [J becomes I2-(I1+1)] I2-(I1+1) > -1 These are the Constraints

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Error Checking Artificial constraints are created to aid in finding some types of errors For instance, array bounds checking When element X(i) of a 100-element array is referenced, constraints S(i) 100 are created If these constraints are consistent with the existing ones, we have a problem

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End: Phase 2: Symbolic Execution Generate Symbolic Representation, Detect some types of errors

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Phase 3: Inequality Solver Generate Symbolic Representation, Detect some types of errors

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How the Inequality Solver works Constraints from previous phase For example, I1+1 -1 Finds values that satisfy the constraints, using linear programming algorithm (Glover) These sets of values are our test data

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How the Inequality Solver works Constraints to be satisfied: I1 + 1 <= I2 I2 – (I1 + 1) > -1 Possible to find values? Yes – 0 and 1, for instance. So, constraints are consistent. So, control path 1-5, 7, 9 executable for values that satisfy constraints.

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How the Inequality Solver works Constraints to be satisfied: I1 + 1 > I2 I1 + 1 - I2 <= -1 Possible to find values? Constraints are inconsistent. So, control path 1-3, 6-9 non-executable for any values of J and K.

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End: Phase 3: Inequality Solver Generate Symbolic Representation, Detect some types of errors Generate Test Data, Find Non-executable Paths

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Limitations System requires each path to be completely specified Path constraints must be linear Input and output statements are ignored

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Related Work DAVE (Osterweil, Fosdick) – analyzes data flow and finds data flow anomalies between subprograms PET (Stucki) – maintains relevant information (execution count, min and max values) about statements ACES (Ramamoorthy et al.) - detects unreliable program constructs EFFIGY (King) – represents a path's computations by symbolically executing a path SELECT (Stanford Research Institute) – attempts to generate test data and verify assertions for program inputs

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