scholarly journals Timed ATL: Forget Memory, Just Count

2019 ◽  
Vol 66 ◽  
pp. 197-223
Author(s):  
Michal Jozef Knapik ◽  
Etienne Andre ◽  
Laure Petrucci ◽  
Wojciech Jamroga ◽  
Wojciech Penczek
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Discrete Time ◽  
The Other ◽  
Simple Pattern ◽  
Perfect Recall ◽  
Other Hand ◽  
Compact Representations ◽  
Time Extension ◽  
Number Of Visits

In this paper we investigate the Timed Alternating-Time Temporal Logic (TATL), a discrete-time extension of ATL. In particular, we propose, systematize, and further study semantic variants of TATL, based on different notions of a strategy. The notions are derived from different assumptions about the agents’ memory and observational capabilities, and range from timed perfect recall to untimed memoryless plans. We also introduce a new semantics based on counting the number of visits to locations during the play. We show that all the semantics, except for the untimed memoryless one, are equivalent when punctuality constraints are not allowed in the formulae. In fact, abilities in all those notions of a strategy collapse to the “counting” semantics with only two actions allowed per location. On the other hand, this simple pattern does not extend to the full TATL. As a consequence, we establish a hierarchy of TATL semantics, based on the expressivity of the underlying strategies, and we show when some of the semantics coincide. In particular, we prove that more compact representations are possible for a reasonable subset of TATL specifications, which should improve the efficiency of model checking and strategy synthesis.

A LOGIC BASED APPROACH TO PLANNING FOR SPECIFYING A CLASS OF TEMPORALLY EXTENDED GOALS

2004 ◽  
Vol 13 (03) ◽  
pp. 469-485 ◽  
Author(s):  
RAJDEEP NIYOGI
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Polynomial Time ◽  
Linear Temporal Logic ◽  
The Other ◽  
Logical Framework ◽  
Branching Time ◽  
Optimal Plan ◽  
Other Hand ◽  
Planning Procedure

Planning with temporally extended goals has recently been the focus of much attention to researchers in the planning community. We study a class of planning goals where in addition to a main goal there exist other goals, which we call auxiliary goals, that act as constraints to the main goal. Both these type of goals can, in general, be a temporally extended goal. Linear temporal logic (LTL) is inadequate for specification of the overall goals of this type, although, for some situations, it is capable of expressing them separately. A branching-time temporal logic, like CTL, on the other hand, can be used for specifying these goals. However, we are interested in situations where an auxiliary goal has to be satisfiable within a fixed bound. We show that CTL becomes inadequate for capturing these situations. We bring out an existing logic, called min-max CTL, and show how it can effectively be used for the planning purpose. We give a logical framework for expressing the overall planning goals. We propose a sound and complete planning procedure that incorporates a model checking technology. Doing so, we can answer such planning queries as plan existence at the onset besides producing an optimal plan (if any) in polynomial time.

scholarly journals An alternating-time temporal logic with knowledge, perfect recall and past: axiomatisation and model-checking

2011 ◽  
Vol 21 (1) ◽  
pp. 93-131 ◽  
Author(s):  
Dimitar P. Guelev ◽  
Catalin Dima ◽  
Constantin Enea
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Perfect Recall

scholarly journals Discrete-TimeH∞Preview Control Problem in Finite Horizon

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hongxia Wang ◽  
Huanshui Zhang ◽  
Lihua Xie
Keyword(s):  
Game Theory ◽  
Dynamic Programming ◽  
Control Problem ◽  
Discrete Time ◽  
Finite Horizon ◽  
The Other ◽  
Preview Control ◽  
Discrete Time Systems ◽  
Other Hand ◽  
Time Systems

This paper considers theH∞preview control problem for discrete-time systems. It investigates the problem via game theory and dynamic programming. Different from the existing results, on one hand, the proposed approach is suitable for dealing with the corresponding multiple preview channels problem; on the other hand, the approach provides a possibility in explaining how the preview controller improves theH∞performance and why the performance will be saturated.

scholarly journals Limit theorems for the interference terms of discrete-time quantum walks on the line

2013 ◽  
Vol 13 (7&8) ◽  
pp. 661-671
Author(s):  
Takuya Machida
Keyword(s):  
Density Matrix ◽  
Discrete Time ◽  
Limit Theorems ◽  
Probability Distributions ◽  
Quantum Walks ◽  
The Other ◽  
Density Matrices ◽  
Other Hand ◽  
Time Quantum

The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal elements of the density matrix. On the other hand, although off-diagonal parts of the density matrices have an important role to quantify quantumness, they have not received attention in quantum walks. We focus on the off-diagonal parts of the density matrices for discrete-time quantum walks on the line and derive limit theorems for them.

scholarly journals Relationships Between Two Definitions of Fading Memory for Discrete-Time Systems

2015 ◽  
Vol 61 (4) ◽  
pp. 377-380
Author(s):  
Andrzej Borys
Keyword(s):  
Discrete Time ◽  
The Other ◽  
Fading Memory ◽  
Memory Property ◽  
Discrete Time Systems ◽  
Other Hand ◽  
Time Systems ◽  
Time Point

Abstract In this paper, we refer to two definitions of fading memory property, which were published in the literature, for discrete-time circuits and systems. One of these definitions relates to systems working with signals (sequences) defined for both the positive and negative integers, expanding from minus infinity to plus infinity. On the other hand, the second one refers to systems processing sequences defined only for nonnegative integers, that is starting at the discrete-time point equal to zero and expanding to plus infinity. We show here that the second definition follows from the first one. That is they are not independent. Moreover, we also show that if an operator describing a system possesses a fading memory according to the second definition, then its associated operator has this property, too, but in accordance with the first definition.

scholarly journals X and more Parallelism. Integrating LTL-Next into SAT-based Planning with Trajectory Constraints while Allowing for even more Parallelism

2018 ◽  
Vol 21 (62) ◽  
pp. 75
Author(s):  
Gregor Behnke ◽  
Susanne Biundo
Keyword(s):  
Temporal Logic ◽  
State Of The Art ◽  
Empirical Evaluation ◽  
Linear Temporal Logic ◽  
Boolean Satisfiability ◽  
The Other ◽  
Major Drawback ◽  
Current State ◽  
Other Hand ◽  
Compilation Techniques

Linear temporal logic (LTL) provides expressive means to specify temporally extended goals as well as preferences.Recent research has focussed on compilation techniques, i.e., methods to alter the domain ensuring that every solution adheres to the temporally extended goals.This requires either new actions or an construction that is exponential in the size of the formula.A translation into boolean satisfiability (SAT) on the other hand requires neither.So far only one such encoding exists, which is based on the parallel $\exists$-step encoding for classical planning.We show a connection between it and recently developed compilation techniques for LTL, which may be exploited in the future.The major drawback of the encoding is that it is limited to LTL without the X operator.We show how to integrate X and describe two new encodings, which allow for more parallelism than the original encoding.An empirical evaluation shows that the new encodings outperform the current state-of-the-art encoding.

scholarly journals The Refined Best Reply Correspondence and Backward Induction

2019 ◽  
Vol 20 (1) ◽  
pp. 52-66
Author(s):  
Dieter Balkenborg ◽  
Christoph Kuzmics ◽  
Josef Hofbauer
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
The Other ◽  
Backward Induction ◽  
Perfect Recall ◽  
Extensive Form ◽  
Remarkable Property ◽  
Extensive Form Games ◽  
Other Hand ◽  
Perfect Equilibria

Abstract Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg et al. (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense, fixed points of this correspondence refine even trembling hand perfect equilibria, while, on the other hand, reasonable equilibria that are not weak perfect Bayesian equilibria are fixed points of this correspondence.

scholarly journals Alternating-time Temporal Logic on Finite Traces

2018 ◽  
Author(s):  
Francesco Belardinelli ◽  
Alessio Lomuscio ◽  
Aniello Murano ◽  
Sasha Rubin
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Optimal Algorithms ◽  
Branching Time ◽  
Multi Agent Systems ◽  
Perfect Recall ◽  
Agent Systems ◽  
Imperfect Recall ◽  
Multi Agent

We develop a logic-based technique to analyse finite interactions in multi-agent systems. We introduce a semantics for Alternating-time Temporal Logic (for both perfect and imperfect recall) and its branching-time fragments in which paths are finite instead of infinite.  We study validities of these logics and present optimal algorithms for their model-checking problems in the perfect recall case.

scholarly journals Temporal Logic Trees for Model Checking and Control Synthesis of Uncertain Discrete-time Systems

2021 ◽  
pp. 1-1
Author(s):  
Yulong Gao ◽  
Alessandro Abate ◽  
Frank J. Jiang ◽  
Mirco Giacobbe ◽  
Lihua Xie ◽  
...  
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Discrete Time ◽  
Control Synthesis ◽  
Discrete Time Systems ◽  
And Control ◽  
Time Systems
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