On the Satisfiability and Model Checking for one Parameterized Extension of Linear-time Temporal Logic

Sequential reactive systems are computer programs or hardware devices which process the flows of input data or control signals and output the streams of instructions or responses. When designing such systems one needs formal specification languages capable of expressing the relationships between the input and output flows. Previously, we introduced a family of such specification languages based on temporal logics $LTL$, $CTL$ and $CTL^*$ combined with regular languages. A characteristic feature of these new extensions of conventional temporal logics is that temporal operators and basic predicates are parameterized by regular languages. In our early papers, we estimated the expressive power of the new temporal logic $Reg$-$LTL$ and introduced a model checking algorithm for $Reg$-$LTL$, $Reg$-$CTL$, and $Reg$-$CTL^*$. The main issue which still remains unclear is the complexity of decision problems for these logics. In the paper, we give a complete solution to satisfiability checking and model checking problems for $Reg$-$LTL$ and prove that both problems are Pspace-complete. The computational hardness of the problems under consideration is easily proved by reducing to them the intersection emptyness problem for the families of regular languages. The main result of the paper is an algorithm for reducing the satisfiability of checking $Reg$-$LTL$ formulas to the emptiness problem for Buchi automata of relatively small size and a description of a technique that allows one to check the emptiness of the obtained automata within space polynomial of the size of input formulas.

Specifying with Interface and Trait Abstractions in Abstract State Machines: A Controlled Experiment

State Machine (ASM) theory is a well-known state-based formal method. As in other state-based formal methods, the proposed specification languages for ASMs still lack easy-to-comprehend abstractions to express structural and behavioral aspects of specifications. Our goal is to investigate object-oriented abstractions such as interfaces and traits for ASM-based specification languages. We report on a controlled experiment with 98 participants to study the specification efficiency and effectiveness in which participants needed to comprehend an informal specification as problem (stimulus) in form of a textual description and express a corresponding solution in form of a textual ASM specification using either interface or trait syntax extensions. The study was carried out with a completely randomized design and one alternative (interface or trait) per experimental group. The results indicate that specification effectiveness of the traits experiment group shows a better performance compared to the interfaces experiment group, but specification efficiency shows no statistically significant differences. To the best of our knowledge, this is the first empirical study studying the specification effectiveness and efficiency of object-oriented abstractions in the context of formal methods.

From parametric trace slicing to rule systems

Parametric runtime verification is the process of verifying properties of execution traces of (data carrying) events produced by a running system. This paper continues our work exploring the relationship between specification techniques for parametric runtime verification. Here we consider the correspondence between trace-slicing automata-based approaches and rule systems. The main contribution is a translation from quantified automata to rule systems, which has been implemented in Scala. This then allows us to highlight the key differences in how the two formalisms handle data, an important step in our wider effort to understand the correspondence between different specification languages for parametric runtime verification. This paper extends a previous conference version of this paper with further examples, a proof of correctness, and an optimisation based on a notion of redundancy observed during the development of the translation.

Fraïssé–Hintikka theorem in institutions

We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbitrary institutions whose sentences are finitary. These include many-sorted first-order logic, higher-order logic with types, as well as a number of other logics arising in connection to specification languages. The gain for the classical case is that the characterization is proved directly for all signatures, including infinite ones.