In this paper, we integrate separation logic with Propositional Projection Temporal Logic (PPTL) to obtain a two-dimensional logic, namely PPTL. The spatial dimension is realized by a decidable fragment of separation logic which can be used to describe linked lists, and the temporal dimension is expressed by PPTL. We show that PPTL and PPTL are closely related in their syntax structures. That i...

To model and verify multi-core parallel programs, the paper proposes an axiom system for Propositional Projection Temporal Logic with Cylinder Computation Model (CCM-PPTL). To do so, the syntax and semantics of CCM-PPTL are presented. Further, based on the logical laws of PPTL, some algebraic laws of sequence expressions and logical laws regarding CCM operators are proved. Moreover, the axiom s...

This paper presents a case study for symbolic model checking (SMC) with Propositional Projection Temporal Logic (PPTL). First, PPTL is briefly introduced. Then an outline of symbolic model checking algorithm for PPTL proposed in [21] is presented. As a case study, a single-track railroad crossing control system (STRCCS) is employed to illustrate how SMC for PPTL can be utilized in the specifica...

This paper investigates the complexity of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Propositional Projection Temporal Logic (PPTL) is first extended to include projection star. Then, by reducing the emptiness problem of star-free expressions to the problem of the satisfiability of PPTL* formulas, the lower bound of the complexity for the satisfiability of PPTL* for...

The paper presents a proof system for Propositional Projection Temporal Logic (PPTL) with projection-plus. The syntax, semantics, and logical laws of PPTL are introduced together with an axiom system consisting of axioms and inference rules. To facilitate proofs, some of the frequently used theorems are proved. A normal form of PPTL formulas is presented, and the soundness and completeness of t...

This paper investigates model-checking Needham-Schroeder Public-Keyprotocol using Propositio nal Projection Temporal Logic (PPTL). To this end, the ProMeLa model of the protocol is firstly constructed then the properties to verify is specified by PPTL formulas, which is translated into automata and further to Never Claim. The transformation is by the method we present and is implemented by an a...

Propositional Projection Temporal Logic (PPTL) is a useful formalism for reasoning about period of time in hardware and software systems and can handle both sequential and parallel compositions. In this paper, based on discrete time Markov chains, we investigate the probabilistic model checking approach for PPTL towards verifying arbitrary linear-time properties. We first define a normal form g...

This paper investigates compositional verification with Propositional Projection Temporal Logic (PPTL). To this end, a sublogic Stutter-invariant PPTL (written as PPTLst) is first proposed. As a specification language, PPTLst helps designers get rid of irrelevant detail in compositional verification of a concurrent system since the projection construct of PPTLst allows designers to assert formu...

Temporal logics are widely adopted in Artificial Intelligence (AI) planning for specifying Search Control Knowledge (SCK). However, traditional temporal logics are limited in expressive power since they are unable to express spatial constraints which are as important as temporal ones in many planning domains. To this end, we propose a twodimensional (spatial and temporal) logic namely PPTL by t...

Propositional Projection Temporal Logic (PPTL) is a useful formalism for reasoning about period of time in hardware and software systems and can handle both sequential and parallel compositions. In this paper, based on discrete time Markov chains, we investigate the probabilistic model checking approach for PPTL towards verifying arbitrary linear-time properties. We first define a normal form g...