Common use of Abstraction Clause in Contracts

Abstraction. As stated in the introduction, the strength of model learning is that it can produce simple models of complex systems. This, of course, depends on the application of an appropriate abstraction. In the above description of model learning, such an abstraction is hidden in functions beh and xxxX . While in practice, xxxX usually is the semantics associated with the class of models that is inferred by some learning algorithm, the function beh abstracts the actual observable behavior of a program to the level of this semantics. Angluin’s MAT framework, e.g., has been implemented for Xxxxx machine models over finite sets of inputs and outputs [46], where xxxX is a mapping from sequences of inputs to outputs. On the other hand, learning Xxxxx machine models of realistic software components requires a test harness which translates the abstract sequences of inputs to concrete seqeuences of method invocations on the component interface, and abstracts concrete return values of invocations to abstract outputs. The choice of a class of models requires the existence of a learning algo- rithm for this class of models as well as the definition of a function beh that abstracts concrete program executions to traces in the semantics of this class of models. Defining such an appropriate abstraction beh oftentimes is not trivial as it is required to be deterministic and determines the aspects of a component’s behavior that becomes observable. The extension of learning algorithms to richer classes of models is an effort that has two positive impacts in this scenario: On the one hand, using more expressive classes of models can help representing more interesting aspects of a component’s behavior in a model. On the other hand, using more expres- sive models can mitigate the laborious and often error-prone burden of defining appropriate functions beh. This has led to multiple lines of works that extend Angluin’s MAT framework to richer classes of models — most notably classes that can describe control-flow as well as data-flow or timing information. Extensions require finding right- congruences for more expressive classes of automata. One principal challenge that all these works face is that in a black-box setting, models can only be learned from observable behavior. Inferring complex causal relations like data manipu- lations or timed behavior quickly requires many queries and often has principle

Abstraction. As stated in the introduction, the strength of model learning is that it can produce simple models of complex systems. This, of course, depends on the application of an appropriate abstraction. In the above description of model learning, such an abstraction is hidden in functions beh and xxxX . While in practice, xxxX usually is the semantics associated with the class of models that is inferred by some learning algorithm, the function beh abstracts the actual observable behavior of a program to the level of this semantics. Angluin’s MAT framework, e.g., has been implemented for Xxxxx machine models over finite finite sets of inputs and outputs [46], where xxxX is a mapping from sequences of inputs to outputs. On the other hand, learning Xxxxx machine models of realistic software components requires a test harness which translates the abstract sequences of inputs to concrete seqeuences of method invocations on the component interface, and abstracts concrete return values of invocations to abstract outputs. The choice of a class of models requires the existence of a learning algo- rithm for this class of models as well as the definition definition of a function beh that abstracts concrete program executions to traces in the semantics of this class of models. Defining Defining such an appropriate abstraction beh oftentimes is not trivial as it is required to be deterministic and determines the aspects of a component’s behavior that becomes observable. The extension of learning algorithms to richer classes of models is an effort effort that has two positive impacts in this scenario: On the one hand, using more expressive classes of models can help representing more interesting aspects of a component’s behavior in a model. On the other hand, using more expres- sive models can mitigate the laborious and often error-prone burden of defining defining appropriate functions beh. This has led to multiple lines of works that extend Angluin’s MAT framework to richer classes of models — most notably classes that can describe control-flow control-flow as well as data-flow data-flow or timing information. Extensions require finding finding right- congruences for more expressive classes of automata. One principal challenge that all these works face is that in a black-box setting, models can only be learned from observable behavior. Inferring complex causal relations like data manipu- lations or timed behavior quickly requires many queries and often has principle