Finite-Trace Linear Temporal Logic: Coinductive Completeness

2016 ◽  
pp. 333-350 ◽  
Author(s):  
Grigore Roşu
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Finite Trace

scholarly journals Finite-Trace and Generalized-Reactivity Specifications in Temporal Synthesis

2021 ◽  
Author(s):  
Giuseppe De Giacomo ◽  
Antonio Di Stasio ◽  
Lucas M. Tabajara ◽  
Moshe Vardi ◽  
Shufang Zhu
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Specification Language ◽  
Ai Planning ◽  
Success Stories ◽  
Ltl Synthesis ◽  
Finite Trace

Linear Temporal Logic (LTL) synthesis aims at automatically synthesizing a program that complies with desired properties expressed in LTL. Unfortunately it has been proved to be too difficult computationally to perform full LTL synthesis. There have been two success stories with LTL synthesis, both having to do with the form of the specification. The first is the GR(1) approach: use safety conditions to determine the possible transitions in a game between the environment and the agent, plus one powerful notion of fairness, Generalized Reactivity(1), or GR(1). The second, inspired by AI planning, is focusing on finite-trace temporal synthesis, with LTLf (LTL on finite traces) as the specification language. In this paper we take these two lines of work and bring them together. We first study the case in which we have an LTLf agent goal and a GR(1) assumption. We then add to the framework safety conditions for both the environment and the agent, obtaining a highly expressive yet still scalable form of LTL synthesis.

scholarly journals Divergent stutter bisimulation abstraction for controller synthesis with linear temporal logic specifications

Automatica ◽  
2021 ◽  
Vol 130 ◽  
pp. 109723
Author(s):  
Sahar Mohajerani ◽  
Robi Malik ◽  
Andrew Wintenberg ◽  
Stéphane Lafortune ◽  
Necmiye Ozay
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Controller Synthesis

scholarly journals A Unified Translation of Linear Temporal Logic to ω-Automata

2020 ◽  
Vol 67 (6) ◽  
pp. 1-61
Author(s):  
Javier Esparza ◽  
Jan Křetínský ◽  
Salomon Sickert
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic

Extending Linear Temporal Logic with Clocks to Object-Z

2014 ◽  
Vol 513-517 ◽  
pp. 927-930
Author(s):  
Zhi Cheng Wen ◽  
Zhi Gang Chen
Keyword(s):  
Real Time ◽  
Temporal Logic ◽  
Formal Specification ◽  
Large Scale ◽  
Linear Temporal Logic ◽  
Specification Language ◽  
Continuous Variables ◽  
Real Time System ◽  
Software Specification ◽  
Formal Specification Language

Object-Z, an extension to formal specification language Z, is good for describing large scale Object-Oriented software specification. While Object-Z has found application in a number of areas, its utility is limited by its inability to specify continuous variables and real-time constraints. Linear temporal logic can describe real-time system, but it can not deal with time variables well and also can not describe formal specification modularly. This paper extends linear temporal logic with clocks (LTLC) and presents an approach to adding linear temporal logic with clocks to Object-Z. Extended Object-Z with LTLC, a modular formal specification language, is a minimum extension of the syntax and semantics of Object-Z. The main advantage of this extension lies in that it is convenient to describe and verify the complex real-time software specification.

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

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