## Discounting the future in systems theory (2003)

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Venue: | In Automata, Languages, and Programming, LNCS 2719 |

Citations: | 45 - 16 self |

### BibTeX

@INPROCEEDINGS{Alfaro03discountingthe,

author = {Luca De Alfaro and Thomas A. Henzinger and Rupak Majumdar},

title = {Discounting the future in systems theory},

booktitle = {In Automata, Languages, and Programming, LNCS 2719},

year = {2003},

pages = {1022--1037},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1511 |
The Temporal Logic of Reactive and Concurrent Systems:Specification
- Manna, Pnueli
- 1992
(Show Context)
Citation Context ...s and games, are important in many computer science applications, and the ω-regular properties offer an accomplished theory for their analysis. The theory is expressive from a practical point of view =-=[22, 27]-=-, computational (algorithmic) [5, 28], and abstract (language-independent) [21, 34]. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-bas... |

1223 |
The Temporal Logic of Programs
- Pnueli
- 1977
(Show Context)
Citation Context ...s and games, are important in many computer science applications, and the ω-regular properties offer an accomplished theory for their analysis. The theory is expressive from a practical point of view =-=[22, 27]-=-, computational (algorithmic) [5, 28], and abstract (language-independent) [21, 34]. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-bas... |

448 | Alternating-time Temporal Logic
- Alur, Henzinger, et al.
(Show Context)
Citation Context ...ion, and thus ensures the duality of the two pre operators. By specializing the quantitative pre operators Qpre i to turn-based deterministic game structures, we obtain the controllable pre operators =-=[2]-=- Cpre i: FB ↦→ FB, which are closed on boolean regions. In particular, for every boolean region f ∈ FB and state s ∈ Q, Cpre 1(f)(s) = 1 iff ∃γ1 ∈ Γ1(s). ∀γ2 ∈ Γ2(s). f(δ(s, γ1, γ2)) = 1. In words, fo... |

299 |
Results on the propositional µ-calculus
- Kozen
- 1983
(Show Context)
Citation Context ... property values from both directions. The key insight of this work is that discounting is most naturally and fundamentally applied not to properties, nor to state equivalences, but to the µ-calculus =-=[20]-=-. We introduce the discounted µ-calculus, a quantitative fixpoint calculus: rather than computing with sets of states, as the traditional µ-calculus does, we compute with functions that assign to each... |

271 | Probabilistic simulations for probabilistic processes
- Segala, Lynch
- 1995
(Show Context)
Citation Context ...layer game structures), for a < 1, discounted game bisimulation coincides with the discounted bisimulation of [12], and undiscounted game bisimulation coincides with the probabilistic bisimulation of =-=[30]-=-. On transition systems (one-player deterministic game structures), undiscounted game bisimulation coincides with classical bisimulation [24]. However, undiscounted 3 Bisimilarity is usually considere... |

260 | Results on the propositional -calculus - Kozen - 1983 |

254 |
Game Theory
- Owen
- 1995
(Show Context)
Citation Context ...l expected reward for player 1) of a matrix game. The minmax theorem guarantees that this matrix game has optimal strategies for both players [35]. The matrix game can be solved by linear programming =-=[9, 26]-=-. The player 2 operator Qpre 2 is defined symmetrically. The minmax theorem permits the exchange of the sup and inf in the definition, and thus ensures the duality of the two pre operators. By special... |

240 |
Modeling and verification of randomized distributed real-time systems
- SEGALA
- 1995
(Show Context)
Citation Context ...ralize finite behavior by considering behavior at infinity, they can distinguish behavior differences that occur arbitrarily late. This exactness becomes even more pronounced for probabilistic models =-=[6, 29, 33]-=-, whose behaviors are specified using numerical quantities, because the theory can distinguish arbitrarily small perturbations of a system. We propose an alternative formalism that is (in a certain se... |

240 |
Stochastic games
- Shapley
- 1953
(Show Context)
Citation Context ... pseudometrics on states. Both are achieved by defining a discounted version of the classical theory. Discounting is inspired by similar ideas in Markov decision processes, economics, and game theory =-=[16, 31]-=-, and captures the natural engineering intuition that the far-away future is not as important as the near future. Consider, for example, the safety property that no unsafe state is visited. In the cla... |

227 |
Competitive Markov decision processes
- Filar, Vrieze
- 1996
(Show Context)
Citation Context ... pseudometrics on states. Both are achieved by defining a discounted version of the classical theory. Discounting is inspired by similar ideas in Markov decision processes, economics, and game theory =-=[16, 31]-=-, and captures the natural engineering intuition that the far-away future is not as important as the near future. Consider, for example, the safety property that no unsafe state is visited. In the cla... |

225 |
Efficient Model Checking in fragments of the propositional mu-calculus (extended abstract
- Emerson, Lei
- 1986
(Show Context)
Citation Context ... 28], and abstract (language-independent) [21, 34]. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution =-=[13, 15]-=-, and property-preserving equivalence relations between structures [4, 24]. From a systems engineering point of view, however, the theory has a significant drawback: it is too exact [1]. Since the ωre... |

218 |
Automatic verification of probabilistic concurrent finite-state programs
- VARDI
- 1985
(Show Context)
Citation Context ...ralize finite behavior by considering behavior at infinity, they can distinguish behavior differences that occur arbitrarily late. This exactness becomes even more pronounced for probabilistic models =-=[6, 29, 33]-=-, whose behaviors are specified using numerical quantities, because the theory can distinguish arbitrarily small perturbations of a system. We propose an alternative formalism that is (in a certain se... |

154 | On the synthesis of strategies in infinite games
- Thomas
- 1995
(Show Context)
Citation Context ...ructures [9, 16]. These structures generalize several standard models of computation, including nondeterministic transition systems, Markov decision processes [10], and deterministic two-player games =-=[2, 32]-=-. The use of discounting gives our theory two main features: computationality and robustness. Computationality is due to the fact that discount factors strictly less than 1 ensure the geometric conver... |

139 |
On a decision method in restricted second-order arithmetic
- Büchi
- 1962
(Show Context)
Citation Context ...puter science applications, and the ω-regular properties offer an accomplished theory for their analysis. The theory is expressive from a practical point of view [22, 27], computational (algorithmic) =-=[5, 28]-=-, and abstract (language-independent) [21, 34]. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution [13,... |

135 |
O.: Characterizing finite Kripke structures in propositional temporal logic. Theoretical Computer Science 59
- Browne, Clarke, et al.
- 1988
(Show Context)
Citation Context ... the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution [13, 15], and property-preserving equivalence relations between structures =-=[4, 24]-=-. From a systems engineering point of view, however, the theory has a significant drawback: it is too exact [1]. Since the ωregular properties generalize finite behavior by considering behavior at inf... |

125 |
Operational and algebraic semantics of concurrent processes
- Milner
- 1201
(Show Context)
Citation Context ... the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution [13, 15], and property-preserving equivalence relations between structures =-=[4, 24]-=-. From a systems engineering point of view, however, the theory has a significant drawback: it is too exact [1]. Since the ωregular properties generalize finite behavior by considering behavior at inf... |

117 | Alternating refinement relations
- Alur, Henzinger, et al.
- 1998
(Show Context)
Citation Context ... setup, the distance function that considers all states to be equivalent in the boolean sense is the least distance function. ⎪⎭sgame bisimulation is not equivalent to the alternating bisimulation of =-=[3]-=-, which has been defined for deterministic game structures. By the minimax theorem [35], we can exchange the two middle sup and inf operators in the definition of Fa; that is, the roles of players 1 a... |

96 |
A Probabilistic PDL
- Kozen
- 1985
(Show Context)
Citation Context ...32780, the DARPA grant F33615-C-98-3614, the NSF grants CCR-9988172, CCR-0234690 and CCR-0225610, and the ONR grant N00014-02-1-0671.sthe value of a property to be a real number in the interval [0,1] =-=[19]-=-. Second, we generalize, as in [11, 12, 18], the classical notions of state equivalences to pseudometrics on states. Both are achieved by defining a discounted version of the classical theory. Discoun... |

81 |
A Temporal Fixpoint Calculus
- Vardi
- 1988
(Show Context)
Citation Context ... properties offer an accomplished theory for their analysis. The theory is expressive from a practical point of view [22, 27], computational (algorithmic) [5, 28], and abstract (language-independent) =-=[21, 34]-=-. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution [13, 15], and property-preserving equivalence rela... |

70 |
Tree automata, µ-calculus and determinacy
- Emerson, Jutla
- 1991
(Show Context)
Citation Context ... 28], and abstract (language-independent) [21, 34]. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution =-=[13, 15]-=-, and property-preserving equivalence relations between structures [4, 24]. From a systems engineering point of view, however, the theory has a significant drawback: it is too exact [1]. Since the ωre... |

69 |
Equivalences, congruences, and complete axiomatizations for probabilistic processes
- Jou, Smolka
- 1990
(Show Context)
Citation Context ...3614, the NSF grants CCR-9988172, CCR-0234690 and CCR-0225610, and the ONR grant N00014-02-1-0671.sthe value of a property to be a real number in the interval [0,1] [19]. Second, we generalize, as in =-=[11, 12, 18]-=-, the classical notions of state equivalences to pseudometrics on states. Both are achieved by defining a discounted version of the classical theory. Discounting is inspired by similar ideas in Markov... |

64 | On model-checking for fragments of -calculus - Emerson, Jutla, et al. - 1993 |

52 | On model-checking for fragments of µ-calculus
- Emerson, Jutla, et al.
- 1993
(Show Context)
Citation Context ...g games with discounted ω-regular objectives. In the classical setting, the connection is as follows. The solution of a game with an ω-regular winning condition can be written as a µ-calculus formula =-=[13, 14]-=-. The fixpoint formula defines the property: when evaluated on linear traces, it holds exactly on the initial states of the traces that satisfy the property. We extend this correspondence to the disco... |

51 | The metric analogue of weak bisimulation for probabilistic processes
- Desharnais, Gupta, et al.
- 2002
(Show Context)
Citation Context ...3614, the NSF grants CCR-9988172, CCR-0234690 and CCR-0225610, and the ONR grant N00014-02-1-0671.sthe value of a property to be a real number in the interval [0,1] [19]. Second, we generalize, as in =-=[11, 12, 18]-=-, the classical notions of state equivalences to pseudometrics on states. Both are achieved by defining a discounted version of the classical theory. Discounting is inspired by similar ideas in Markov... |

51 |
A hierarchy of temporal properties
- Manna, Pnueli
- 1987
(Show Context)
Citation Context ... properties offer an accomplished theory for their analysis. The theory is expressive from a practical point of view [22, 27], computational (algorithmic) [5, 28], and abstract (language-independent) =-=[21, 34]-=-. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution [13, 15], and property-preserving equivalence rela... |

45 |
Regular Expressions for Infinite Trees and a Standard Form of Automata
- Mostowski
- 1984
(Show Context)
Citation Context ...discounted µ-calculus, and let P be a parameter valuation. For every state s of G, we have {[φ]P}. [φ] G ·,P (s) = sup π1∈Π1 infπ2∈Π2 Eπ1,π2 s Rabin chain conditions. An undiscounted Rabin chain game =-=[13, 25]-=- consists of a concurrent game structure G together with a winning condition � n−1 i=0 (✷✸T2i ∧ ¬✷✸T2i+1), where n > 0 and the Tj’s are propositions with ∅ ⊆ [T2n ] ⊆ [T2n−1 ] ⊆ · · · ⊆ [T0 ] = Q. A m... |

44 | O.: Concurrent reachability games
- Alfaro, Henzinger, et al.
- 2007
(Show Context)
Citation Context ...table set U, a probability distribution on U is a function p: U ↦→ [0, 1] such that u∈U p(u) = 1. We write D(U) for the set of probability distributions on U. A two-player (concurrent) game structure =-=[2, 7]-=- G = 〈Q, M, Γ1, Γ2, δ〉 consists of the following components: – A finite set Q of states. – A finite set M of moves. – Two move assignments Γ1, Γ2: Q ↦→ 2 M \ ∅. For i ∈ {1, 2}, the assignment Γi assoc... |

42 | Metrics for labelled markov systems
- Desharnais, Gupta, et al.
- 1999
(Show Context)
Citation Context ...3614, the NSF grants CCR-9988172, CCR-0234690 and CCR-0225610, and the ONR grant N00014-02-1-0671.sthe value of a property to be a real number in the interval [0,1] [19]. Second, we generalize, as in =-=[11, 12, 18]-=-, the classical notions of state equivalences to pseudometrics on states. Both are achieved by defining a discounted version of the classical theory. Discounting is inspired by similar ideas in Markov... |

33 | Stochastic transition systems
- ALFARO
- 1998
(Show Context)
Citation Context ...ralize finite behavior by considering behavior at infinity, they can distinguish behavior differences that occur arbitrarily late. This exactness becomes even more pronounced for probabilistic models =-=[6, 29, 33]-=-, whose behaviors are specified using numerical quantities, because the theory can distinguish arbitrarily small perturbations of a system. We propose an alternative formalism that is (in a certain se... |

29 | Tree automata, �- calculus and de-terminacy - Emerson, Jutla - 1991 |

27 | Ecient model checking in fragments of the propositional mu-calculus (extended abstract - EL86, Lei - 1986 |

24 | Finite-State Markovian Decision Processes - Derman - 1970 |

19 | T.A.: Finitary fairness
- Alur, Henzinger
- 1994
(Show Context)
Citation Context ... solution [13, 15], and property-preserving equivalence relations between structures [4, 24]. From a systems engineering point of view, however, the theory has a significant drawback: it is too exact =-=[1]-=-. Since the ωregular properties generalize finite behavior by considering behavior at infinity, they can distinguish behavior differences that occur arbitrarily late. This exactness becomes even more ... |

9 | Reasoning about efficiency within a probabilistic µ-calculus
- McIver
- 1998
(Show Context)
Citation Context ... of a formula φ is the quantitative region [φ]E,1 obtained from the parameter valuation 1 that maps every parameter in Λ to 1. The undiscounted semantics coincides with the quantitative µ-calculus of =-=[9, 23]-=-. In the case of turnbased deterministic game structures, it coincides with the alternating-time µ-calculus of [2], and in the case of transition systems, with the classical µ-calculus of [19]. The fo... |

5 |
Automata on Infinite Objects and
- Rabin
- 1972
(Show Context)
Citation Context ...puter science applications, and the ω-regular properties offer an accomplished theory for their analysis. The theory is expressive from a practical point of view [22, 27], computational (algorithmic) =-=[5, 28]-=-, and abstract (language-independent) [21, 34]. In its general setting, the theory considers games with ωregular winning conditions [17, 28], provides fixpoint-based algorithms for their solution [13,... |

4 |
From verification to control: Dynamic programs for ω-regular objectives
- Alfaro, Henzinger, et al.
- 2006
(Show Context)
Citation Context ...ion. For every ɛ > 0, there is a δ > 0 such that for all paths σ1, σ2 ∈ Σ with dC(σ1, σ2) < δ, we have |[φ]P(σ1) − [φ]P(σ2)| < ɛ. A formula φ of the discounted µ-calculus is player-1 strongly guarded =-=[8]-=- if (1) φ is closed and consists of a string of fixpoint quantifiers followed by a quantifier-free part, (2) φ contains no occurrences of pre 2, and (3) every conjunction in φ has at least one constan... |

4 | Quantitative solution of !-regular games - Alfaro, Majumdar - 1998 |

3 | Reasoning about eciency within a probabilistic -calculus - McIver - 1998 |

2 |
Quantitative solution of ω-regular games
- Alfaro, Majumdar
- 2001
(Show Context)
Citation Context ...rather than computing with sets of states, as the traditional µ-calculus does, we compute with functions that assign to each state a value between 0 and 1. A quantitative µ-calculus was introduced in =-=[9]-=- to compute the values of probabilistic ω-regular games by iterating a quantitative version of the predecessor (pre) operator. The discounted µ-calculus is obtained from the calculus of [9] by discoun... |

1 | From verification to control: Dynamic programs for #-regular objectives - Alfaro, Henzinger, et al. - 2001 |