Linear Approximation of Execution Time Constraints

This paper defines an algorithm for predicting worst and best case execution times, and determining execution time constraints, of control-flow paths through real-time programs using their partial correctness semantics. The algorithm produces a linear approximation of path traversal conditions, worst and best case execution times and strongest postconditions for timed paths in abstract real-time programs. We further derive techniques to determine the set of control-flow paths with decidable worst and best case execution times. The approach is based on a weakest liberal precondition semantics and relies on supremum and infimum calculations similar to standard computations from Linear Programming and Presburger Arithmetic. The methodology is generic in that it is applicable to any executable language that can be supplied with a predicate transformer semantics and hence provides a verification basis for high level as well as assembler level execution time analysis techniques

Formal Semantics for Program Paths

This paper provides the syntax and semantics for a systematic approach to the problem of analysing control-flow paths in computer programs. We give an abstract syntax and a partial correctness semantics for program control-flow paths as a generic model for path analysis and constraint derivation. This approach is formally based on a predicate transformer semantics over a boolean-valued predicate space and an abstract command language. The notions of a command, dead commands, the entry and exit conditions of a command and the inverse of a command are formally defined and investigated on the base of the semantics. A notion of command refinement is introduced capturing the abstraction process in program development from specification to implementation with partial correctness. Furthermore, command-reduction theorems and characterisations for command refinement are derived using the underlying semantics. Finally we verify the equivalence of weakest liberal precondition and strongest postcondition semantics for program commands in terms of the ordering relation they define on the command language. The approach is generic in that it is applicable to any program language that can be supplied with a predicate transformer semantics

Refinement and State Machine Abstraction

Precise module interface specifications are essential in modular software development. The role of state in these specifications has been the issue of some debate and is central to the notion of data refinement. In previous work, Hoffman and Strooper introduce a state-abstraction lattice that defines a partial order on specifications for deterministic and complete languages. They use this lattice to define a notion of state abstractness and show that this intuitive notion corresponds to the use of the terms "abstract" and "concrete" as used in data-refinement proofs. In this paper, we extend this work for a class of specifications and languages that we call demonic and semi-deterministic. We also introduce a notion of backward refinement and prove that backward refinement together with the common forward refinement of VDM and Z form a sound and complete refinement technique with respect to a partial order on languages defined by demonic specifications. We illustrate the ideas using simple languages and specifications

Measuring gratitude in Germany: Validation study of the German versions of the Gratitude Questionnaire-Six Item Form (GQ-6-G) and the Multi-Component Gratitude Measure (MCGM-G)

The Gratitude Questionnaire-Six Item Form (GQ-6; McCullough et al., 2002) is a well-established instrument for measuring gratitude. Recently, the Multi-Component Gratitude Measure (MCGM) was developed as a more holistic approach (Morgan et al., 2017). While the GQ-6 mainly focuses on the emotional component of gratitude, the MCGM encompasses conceptual, attitudinal, and behavioral aspects. As of today, there is no validated German measure for gratitude. In order to close that research gap, the present study focused on validating the German versions of the GQ-6 (GQ-6-G) and of the MCGM (MCGM-G). In addition, multi-group comparisons were conducted to test for cultural measurement invariance. Construct validity was tested similar to original validation studies of the two scales focusing on affect, well-being, empathy, anxiety and depression. The online survey was completed in random order by 508 participants. The one-factor model of the GQ-6-G and the hierarchical structure of the MCGM-G could be replicated. However, the model fit of the Gratitude Questionnaire was significantly better after eliminating one item (GQ-5-G). Multi-group comparisons revealed cultural measurement invariance was established for the GQ-5-G and partial measurement invariance for five of six factors of the MCGM-G, respectively. Reliability analyses revealed good internal consistency for both instruments, and measures for criterion-related and discriminant validity have shown hypothesized relationships. Thus, the GQ-5-G and the MCGM-G are two instruments with good reliability and validity for measuring gratitude in Germany

The Grothendieck-Pietsch domination principle for nonlinear summing integral operators

We transform the concept of p-summing operators, 1≤ p < ∞, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Σ,X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domination principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S,X)-spaces. For p-summing Hammerstein operators we derive the existence of control measures and p-summing extensions to B(Σ,X)-spaces

A Theory for Execution Time Derivation in Real-Time Programs

We provide an abstract command language for real-time programs and outline how a partial correctness semantics can be used to compute execution times. The notions of a timed command, refinement of a timed command, the command traversal condition, and the worst-case and best-case execution time of a command are formally introduced and investigated with the help of an underlying weakest liberal precondition semantics. The central result is a theory for the computation of worst-case and best-case execution times from the underlying semantics based on supremum and infimum calculations. The framework is applied to the analysis of a message transmitter program and its implementation