Temporal Team Semantics Revisited

TL;DR

This paper introduces a novel temporal team semantics framework using time evaluation functions to specify asynchronous hyperproperties, overcoming limitations of trace quantifier logics and enabling automata-theoretic analysis.

Contribution

It develops a new foundation for asynchronous hyperproperties via temporal team semantics with TEFs, and provides automata-based translations and decidability results.

Findings

Embeds synchronous TeamLTL into the new logic

Shows high undecidability of model checking for some fragments

Provides automata-theoretic translation for analysis

Abstract

Temporal logics have been studied as an approach to the specification of hyperproperties, resulting in the conception of "hyperlogics". With a few recent exceptions, the hyperlogics thus far developed can only relate different traces of a transition system synchronously. However, important information is contained in the relation between different points in their asynchronous interaction. To specify such "asynchronous hyperproperties", new trace quantifier based hyperlogics have been developed. Yet, hyperlogics with trace quantification cannot express certain requirements that describe the relationships between all executions of a system. Also, these logics induce model checking problems (MC) with prohibitively high complexity costs in the number of quantifier alternations. We study an alternative approach to asynchronous hyperproperties by introducing a novel foundation of temporal team semantics. Team semantics is a logical framework that specifies properties of sets of traces of unbounded size directly, and thus does not have the same limitation as the quantifier based logics mentioned above. We consider temporal team logics which employ quantification over so-called "time evaluation functions" (TEFs) controlling the asynchronous progress of traces instead of quantification over traces. TEFs constitute a novel approach to defining expressive logics for hyperproperties where diverse asynchronous interactions between computations can be formalised and enforced. We show embeddings of synchronous TeamLTL into our new logics. We show that MC for some TeamCTL fragment is highly undecidable. We present a translation from TeamCTL* to Alternating Asynchronous B\"uchi Automata, and obtain decidability results for the path checking problem and restrictions of MC and SAT. Our translation constitutes the first approach to team semantics based on automata-theoretic methods.