1. Formal Verification

2. Background Information Formal verification methods based on theorem proving techniques and model­checking –To prove the absence of errors (in the formal model) –To reason about the behaviors of programs No known generic software verification –Involves complicated proving –Generally cannot be easily and cost-effectively integrated to software and hardware development cycles

3. Major Verification Topics Specification verification Architecture verification General practical issues

4. Architecture Verification Correctness of architecture refinement –A methodology for the correct stepwise refinement of software architectures –Using the approach of architecture refinement patterns that are correctness preserving and compositional

5. Common Architecture Issues From abstract level to concrete level Simple architecture: Box - arrows, representing data component and connections Large architecture: Hierarchical approach

6. Common Architecture Problem Limited utility of architecture hierarchy results from the current level of informality Ambiguity in architecture allows unintended interpretations. May cause erroneous interpretation

7. Architecture Refinement From a abstract architecture to a concrete (lower- level) architecture –Lead to: Fewer architectural design errors Extensive and systematic reuse of design knowledge and proofs

8. Refinement Pattern Approach A pair architecture schemas (homogenous or heterogeneous) Proven to be relatively correct with respect to the given mapping schema

9. Refinement Pattern Requires a special correctness criterion – A special mapping between architectures – Extensive translation: The representation of components, interfaces, and connections Aggregated, decomposed, or eliminated

10. Completeness Assumption Prove that a concrete architecture has all required properties –No new properties can be inferred from the concrete architecture All components, interfaces, and connections intended to be true of the architecture at its level of detail –If a fact is not explicit in the architecture, assume that it is not intended to be true

11. Completeness Assumption Standard way to proof relative correctness –Show that the concrete specification logically implies the abstract specification under a given mapping –Allow additional and specified behaviors, as long as the specified behavior is implemented –No guarantee that negative properties are preserved under refinement Alternative: –Faithful interpretation –Hard and no general proof technique Use preproved refinement patterns

12. Example Use only logical theories for simplicity To show how to systematically and incrementally transform a abstract architecture to its lower-level form Approach: Combining small and local refinement to form the larger composite

13. Example chars code Lexical Analyzer Lexical Parser Analyzer Optimizer Code Generator toksast bindings

14. Architecture as Theories Architecture styles – Operations and axioms Translation to logic – Patterns  logic (theory generation rules) Mapping – Name mapping – Style mapping – Interpretation mapping

15. Architecture Styles Dataflow style: Axioms example -- Every function must at least have one port:

16. Translation to Logic An instance of function declaration schema: –f: Functional_Style!Function [  op: t] The underlying theory contains the same instance of first order sentences:

17. Mapping Name mapping: –c |  m –op |  w Style mapping: –Accepts (_, _) |  Gets (_, _) –Connects (_, _, _) |  Writes (_,_) ^ Reads(_,_) Interpretation mapping = name + style mapping

18. Proving Criterion – All intended to do – Not intended to do

19. Composition Horizontal – Compose instances of refinement patterns to form one large composite refinement Vertical – Most concrete architecture in a hierarchy is correct with respect to the most abstract – Justified since faithful interpretation is transitive

20. Problem Example Concrete architecture 1 – A  B (dataflow connection) Concrete architecture 2 – B  C (dataflow connection) The composition of 1 and 2 is not faithful! – Need new abstract dataflow from A to C

21. Specification Correctness issue Complete specification of program is in terms of hierarchical structure of module specifications Module external specifications are abstract, about module behavior Module internal specifications are descriptions of internal implementations

22. Concurrent System Verification Program is a set of events Interpreted and verified with a formal proof system Internal specification classified as composite or simple Composite: Composed of linked sub-modules, each with external and internal specification

23. External Specification External specification consist of three parts: Behavior: Module delivers to the environment Provide: How modules synchronizes with the environment? Require: Synchronization cooperation the module expects from environment

24. Composite Internal Specification Internal specification of a composite module associates events described in the external specification of the module with events described in the external specifications of the sub- modules Ports: A set of single direction communication channels between the module and its environment Network link: Sub module ports are connected together to form communication channels

25. Composite Module Verification Verification of composite module: 1.External behaviors of the sub-modules plus the network and interface links must imply the external behavior of composite module 2. Provides and requires of the sub modules and composite module must be mutually supportive and complete Mutual support: Sub module provides imply the sub- module requires Complete: Composite require and provide represent the sub-module requires and provides accurately and completely

26. Simple Module Specification Verification Internal specification of a simple system consists of three parts: Program: Internal specification as example Performance: Whether the program is cyclic or terminates and contains an assert statement that describe the history Interpret: Identify ports with subsequences on the history

27. Simple Module Specification Verification Verification of specifications of a simple module: 1.Performance and interpret statements must imply the external behavior 2. Performance and external provide must be established using following axioms: –History sequence axiom –Statement block axiom –Process history axiom

28. Discussion Task of analyzing programs is easier if the program is composed of modules Key importance is to establish specifications Automated verification system can be based on verification rules

29. Related Works Automatic program verifications - verification condition generator EBS, Chen, Yeh, Reed et al Concurrent programs, Hailpern,Owicki, Lamport and Schneider

30. General Discussion Abstract logic component decomposition verification and efficiency analysis Practical tools, such as UML