# Temporal Specifications with Accumulative Values

@article{Boker2011TemporalSW, title={Temporal Specifications with Accumulative Values}, author={Udi Boker and Krishnendu Chatterjee and Thomas A. Henzinger and Orna Kupferman}, journal={2011 IEEE 26th Annual Symposium on Logic in Computer Science}, year={2011}, pages={43-52} }

There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the…

## 19 Citations

Formalizing and Reasoning about Quality

- Computer ScienceICALP
- 2013

By extending the automata-theoretic approach for LTL to a setting that takes quality into an account, it is able to solve the above problems and show that reasoning about LTL has roughly the same complexity as reasoning about traditional LTL.

Synthesis for Multi-weighted Games with Branching-Time Winning Conditions

- Computer SciencePetri Nets
- 2020

This work encodes both problems to the calculation of maximal fixed points on dependency graphs, thus achieving on-the-fly algorithms with the possibility of early termination in both the model checking problem and the synthesis problem.

Controller Synthesis for MDPs and Frequency LTL\GU

- Computer Science, MathematicsLPAR
- 2015

Quantitative extensions of temporal logics have recently
attracted significant attention. In this work, we study
frequency LTL (fLTL), an extension of LTL which allows to speak
about frequencies of…

Formally Reasoning About Quality

- Computer ScienceJ. ACM
- 2016

Two quantitative extensions of Linear Temporal Logic are introduced, one by propositional quality operators and one by discounting operators, and the usefulness of both extensions is demonstrated and the decidability and complexity of the decision and search problems for them are studied.

Reasoning about CTL ∗ with Graded Path Modalities

- Computer Science
- 2015

GCTL∗ is much more expressive than CTL∗ as it adds to it a form of quantitative reasoning, and this is done at no extra cost in computational complexity.

A Temporal Logic with Mean-Payoff Constraints

- EconomicsICFEM
- 2012

This paper proposes an extension of LTL that describes mean-payoff constraints, and develops an algorithm for the emptiness problems of multi-dimensional payoff automata with Buchi acceptance conditions and multi-threshold mean- payoff acceptance conditions.

Weight monitoring with linear temporal logic: complexity and decidability

- Computer ScienceCSL-LICS
- 2014

This paper introduces an extension of linear time logic including past (LTL) with new operators that impose constraints on the accumulated weight along path fragments that cover properties expressible by several recently proposed formalisms.

Discounting in LTL

- Computer ScienceTACAS
- 2014

One direction in this effort is to refine the “eventually” operators of temporal logic to discounting operators: the satisfaction value of a specification is a value in [0,1], where the longer it takes to fulfill eventuality requirements, the smaller the satisfactionvalue is.

Controller Synthesis for MDPs and Frequency LTL$$_{\setminus \mathbf{G}\mathbf U}$$

- Computer Science, MathematicsICLP 2015
- 2015

This work studies frequency LTL fLTL, an extension of LTL which allows to speak about frequencies of events along an execution which is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour.

Quantitative Interprocedural Analysis

- Computer SciencePOPL
- 2015

The quantitative analysis problem for interprocedural control-flow graphs can be solved in polynomial time, and the framework provides a sound approach (no false positives) for the analysis of inefficiently-used containers.

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