Kleene Algebras and Semimodules for Energy Problems

  title={Kleene Algebras and Semimodules for Energy Problems},
  author={Zolt{\'a}n {\'E}sik and Ulrich Fahrenberg and Axel Legay and Karin Quaas},
With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce generalized energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Uncovering a close connection between energy problems and reachability and Buchi acceptance for semiring-weighted automata, we show that these generalized energy problems are decidable. We also provide complexity results for… 

An ω-Algebra for Real-Time Energy Problems

A *-continuous Kleene ω-algebra of real-time energy functions which can be used to model systems which can consume and regain energy depending on available time.

*-Continuous Kleene ω-Algebras for Energy Problems

It is shown here that energy problems can be solved by algebraic manipulations on the transition matrix of energy automata, and general results about certain classes of finitely additive functions on complete lattices are proved.

An omega-Algebra for Real-Time Energy Problems

A *-continuous Kleene omega-algebra of real-time energy functions which can be used to model systems which can consume and regain energy depending on available time.

Verification for Timed Automata Extended with Unbounded Discrete Data Structures

The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable and obtain a strong model that may be used to model real-time programs with procedure calls.

*-Continuous Kleene $\omega$-Algebras

It is shown that *-continuous Kleene $\omega$-algebras give rise to iteration semiring-semimodule pairs and how this work can be applied to solve certain energy problems for hybrid systems.

Well Behaved Transition Systems

The well-quasi-ordering that defines well-structured transition systems (WSTS) is shown not to be the weakest hypothesis that implies decidability of the coverability problem, and coverability decidable for monotone transition systems that only require the absence of infinite antichains.

An Algebraic Approach to Energy Problems II - The Algebra of Energy Functions

It is shown that energy functions form a *-continuous Kleene ω-algebra, as an application of a general result that finitely additive, locally *-closed and T-continuously functions on complete lattices form *- continuous Kleeneπ-algebras.

Quantitative properties of featured automata

A model of featured weighted automata is introduced which combines featured transition systems and (semiring-) weighted automation and applications to minimum reachability and to energy properties are shown.

*-Continuous Kleene ω-Algebras

It is shown that \(^*\)-continuous Kleene \(\omega \)-algebras give rise to iteration semiring-semimodule pairs, and that for Buchi automata over \(*\)-continuous Kleinene algebra, one can compute the associated infinitary power series.

Algebraic Derivation of Until Rules and Application to Timer Verification

Using correspondences betweenlinear temporal logic and modal Kleene Algebra, rules of linear temporal logic involving the until operator are proved in an algebraic manner in order to verify programmable logic controllers.



Infinite Runs in Weighted Timed Automata with Energy Constraints

This work considers automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource, and asks the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints.

On Kleene Algebras and Closed Semirings

  • D. Kozen
  • Mathematics, Computer Science
  • 1990
The literature contains at several inequivalent definitions of Kleene algebras and related algebraic structures: program logic and semantics, relational algebra, automata theory, and the design and analysis of algorithms.

Well-structured transition systems everywhere!

Energy Games in Multiweighted Automata

This work extends energy games to a multiweighted and parameterized setting, allowing them to model systems with multiple quantitative aspects and investigates the tractability of an extension of multi Weighted energy games in the setting of timed automata.

Minimum-Cost Reachability for Priced Timed Automata

This paper proves decidability of the minimum-cost reachability problem by offering an algorithmic solution, which is based on a combination of branch-and-bound techniques and a new notion of priced regions, which allows symbolic representation and manipulation of reachable states together with the cost of reaching them.

An Algebraic Generalization of omega-Regular Languages

This paper gets rid of the idempotency assumption for the semimodule needed at several places in Esik, Kuich, and applies it to languages that contain finite and infinite words.

Verification of Pushdown Systems Using Omega Algebra with Domain

A framework for the verification of pushdown systems based on an extension of Kleene algebra called omega algebra with domain that allows to formulate behavioural properties that refer to both actions and states.

Lower-bound-constrained runs in weighted timed automata

Timed automata with observers under energy constraints

ExPTIME algorithms are proposed to decide the existence of controllers that ensure existence of infinite runs or reachability of some goal location with non-negative observer value all along the run.

Reachability Games on Extended Vector Addition Systems with States

Several decidable and even tractable subcases of this problem of deciding thewinner in two-player turn-based games with zero-reachability and zero-safety objectives obtained by restricting the number of counters and/or the sets of target configurations are identified.