On regular temporal logics with past

The IEEE standardized Property Specification Language, PSL for short, extends the well-known linear-time temporal logic LTL with so-called semi-extended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the hardware design cycle, from specification to verification. In this article, we extend the common core of these specification languages with past operators. We name this extension PPSL. Although all ω-regular properties are expressible in PSL, SVA, and PPSL, past operators often allow one to specify properties more naturally and concisely. In fact, we show that PPSL is exponentially more succinct than the cores of PSL and SVA. On the star-free properties, PPSL is double exponentially more succinct than LTL. Furthermore, we present a translation of PPSL into language-equivalent nondeterministic Büchi automata, which is based on novel constructions for 2-way alternating automata. The upper bound on the size of the resulting nondeterministic Büchi automata obtained by our translation is almost the same as the upper bound for the nondeterministic Büchi automata obtained from existing translations for PSL and SVA. Consequently, the satisfiability problem and the model-checking problem for PPSL fall into the same complexity classes as the corresponding problems for PSL and SV

A Simple Rewrite System for the Normalization of Linear Temporal Logic

In the mid 80s, Lichtenstein, Pnueli, and Zuck showed that every formula of Past LTL (the extension of Linear Temporal Logic with past operators) is equivalent to a conjunction of formulas of the form $\mathbf{G}\mathbf{F} \varphi \vee \mathbf{F}\mathbf{G} \psi$, where $\varphi$ and $\psi$ contain only past operators. Some years later, Chang, Manna, and Pnueli derived a similar normal form for LTL. Both normalization procedures have a non-elementary worst-case blow-up, and follow an involved path from formulas to counter-free automata to star-free regular expressions and back to formulas. In 2020, Sickert and Esparza presented a direct and purely syntactic normalization procedure for LTL yielding a normal form similar to the one by Chang, Manna, and Pnueli, with a single exponential blow-up, and applied it to the problem of constructing a succinct deterministic $\omega$-automaton for a given formula. However, their procedure had exponential time complexity in the best case. In particular, it does not perform better for formulas that are almost in normal form. In this paper we present an alternative normalization procedure based on a simple set of rewrite rules

Monitoring-Oriented Programming: A Tool-Supported Methodology for Higher Quality Object-Oriented Software

This paper presents a tool-supported methodological paradigm for object-oriented software development, called monitoring-oriented programming and abbreviated MOP, in which runtime monitoring is a basic software design principle. The general idea underlying MOP is that software developers insert specifications in their code via annotations. Actual monitoring code is automatically synthesized from these annotations before compilation and integrated at appropriate places in the program, according to user-defined configuration attributes. This way, the specification is checked at runtime against the implementation. Moreover, violations and/or validations of specifications can trigger user-defined code at any points in the program, in particular recovery code, outputting or sending messages, or raising exceptions. The MOP paradigm does not promote or enforce any specific formalism to specify requirements: it allows the users to plug-in their favorite or domain-specific specification formalisms via logic plug-in modules. There are two major technical challenges that MOP supporting tools unavoidably face: monitor synthesis and monitor integration. The former is heavily dependent on the specification formalism and comes as part of the corresponding logic plug-in, while the latter is uniform for all specification formalisms and depends only on the target programming language. An experimental prototype tool, called Java-MOP, is also discussed, which currently supports most but not all of the desired MOP features. MOP aims at reducing the gap between formal specification and implementation, by integrating the two and allowing them together to form a system

Efficient Parallel Path Checking for Linear-Time Temporal Logic With Past and Bounds

Path checking, the special case of the model checking problem where the model under consideration is a single path, plays an important role in monitoring, testing, and verification. We prove that for linear-time temporal logic (LTL), path checking can be efficiently parallelized. In addition to the core logic, we consider the extensions of LTL with bounded-future (BLTL) and past-time (LTL+Past) operators. Even though both extensions improve the succinctness of the logic exponentially, path checking remains efficiently parallelizable: Our algorithm for LTL, LTL+Past, and BLTL+Past is in AC^1(logDCFL) \subseteq NC

Jeeg: Temporal Constraints for the Synchronization of Concurrent Objects

We introduce Jeeg, a dialect of Java based on a declarative replacement of the synchronization mechanisms of Java that results in a complete decoupling of the 'business' and the 'synchronization' code of classes. Synchronization constraints in Jeeg are expressed in a linear temporal logic which allows to effectively limit the occurrence of the inheritance anomaly that commonly affects concurrent object oriented languages. Jeeg is inspired by the current trend in aspect oriented languages. In a Jeeg program the sequential and concurrent aspects of object behaviors are decoupled: specified separately by the programmer these are then weaved together by the Jeeg compiler

Logic-Based Specification Languages for Intelligent Software Agents

The research field of Agent-Oriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research sub-field studies how formal methods can be used for AOSE. This paper presents a detailed survey of six logic-based executable agent specification languages that have been chosen for their potential to be integrated in our ARPEGGIO project, an open framework for specifying and prototyping a MAS. The six languages are ConGoLog, Agent-0, the IMPACT agent programming language, DyLog, Concurrent METATEM and Ehhf. For each executable language, the logic foundations are described and an example of use is shown. A comparison of the six languages and a survey of similar approaches complete the paper, together with considerations of the advantages of using logic-based languages in MAS modeling and prototyping.Comment: 67 pages, 1 table, 1 figure. Accepted for publication by the Journal "Theory and Practice of Logic Programming", volume 4, Maurice Bruynooghe Editor-in-Chie

Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete

A Formal Framework for Concrete Reputation Systems

In a reputation-based trust-management system, agents maintain information about the past behaviour of other agents. This information is used to guide future trust-based decisions about interaction. However, while trust management is a component in security decision-making, many existing reputation-based trust-management systems provide no formal security-guarantees. In this extended abstract, we describe a mathematical framework for a class of simple reputation-based systems. In these systems, decisions about interaction are taken based on policies that are exact requirements on agents’ past histories. We present a basic declarative language, based on pure-past linear temporal logic, intended for writing simple policies. While the basic language is reasonably expressive (encoding e.g. Chinese Wall policies) we show how one can extend it with quantification and parameterized events. This allows us to encode other policies known from the literature, e.g., ‘one-out-of-k’. The problem of checking a history with respect to a policy is efficient for the basic language, and tractable for the quantified language when policies do not have too many variables