Experiments with Reduction Finding

Jordan, Charles; Kaiser, Łukasz

doi:10.1007/978-3-642-39071-5_15

Cited by 19 publications

(26 citation statements)

References 15 publications

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“…Then, ϕ sigma(aaa)≥2 ∈ Φ r u,v as σ (aaa, u) = 2, σ (aaa, v) = 1, and σ (aaa, v) < n ≤ min (3,2). Besides, ϕ d(min,max) ≥10 ∈ Φ r u,v because |u| > |v| and 9 ≤ 10 ≤ min (16,11). Now, we show results ensuring adequate properties of distinguishability formulas.…”

Section: Distinguishability Formulasmentioning

confidence: 68%

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On Finding a First-Order Sentence Consistent with a Sample of Strings

Rocha

Martins

Ferreira

2018

Electron. Proc. Theor. Comput. Sci.

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We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite structures with unary predicates to denote symbols in an alphabet, and a successor relation. We use results of the Ehrenfeucht-Fraïssé game over successor string structures in order to design an algorithm to find such sentence. We use conditions characterizing the winning strategies for the Spoiler on successor strings structures in order to define formulas which distinguish two strings. Our algorithm returns a boolean combination of such formulas.

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Section: Distinguishability Formulasmentioning

confidence: 68%

“…This algorithm is applied in a general system for learning formulas defining board game rules. These results are also used in finding reductions and polynomial-time programs [11,12]. The work in [17] investigates a variation of the problem introduced in [13] when the class of structures is fixed.…”

Section: Stringmentioning

confidence: 99%

On Finding a First-Order Sentence Consistent with a Sample of Strings

Rocha

Martins

Ferreira

2018

Electron. Proc. Theor. Comput. Sci.

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“…In particular, Constraints (17), (18) and (19) are used to propagate the constraints on r x,q,q 2 , based on the synchronous product construction and the inductive definition of reachability. Based on Constraints (17), (18) and (19), Constraints (20) are used to ensure L(S G) ⊆ L(G 2 ). Let φ S T right denote the resultant formula after combining Constraints (16), (17), (18), (19) and (20).…”

Section: Bounded Resilient Supervisor Synthesismentioning

confidence: 99%

“…Based on Constraints (17), (18) and (19), Constraints (20) are used to ensure L(S G) ⊆ L(G 2 ). Let φ S T right denote the resultant formula after combining Constraints (16), (17), (18), (19) and (20).…”

Section: Bounded Resilient Supervisor Synthesismentioning

confidence: 99%

Towards Bounded Synthesis of Resilient Supervisors

Lin

Zhu

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this work, we study the safety approach of synthesizing resilient supervisors against actuator attacks, for cyber-physical systems that can be modeled as discrete-event systems. A constraint based approach for the bounded synthesis of resilient supervisors is developed. The supervisor obfuscation problem, which is proposed in a specific setting of actuator attack, can be naturally modelled and solved using the same approach.

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“…In the remaining of this section, we will study the following two related problems. A) Given any candidate reduction P of ∆, which we would like to refute via L cand , we only need to show L cand is 14 We shall provide an analysis later in Example 24.…”

Section: A Candidate Counter Examples For Reduction Refutationmentioning

confidence: 99%

Automatic Generation of Optimal Reductions of Distributions

Lin

Masopust

Wonham

et al. 2019

IEEE Trans. Automat. Contr.

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A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable with respect to the source distribution if and only if it is decomposable with respect to each smaller sized distribution (in the reduction). The notion of reduction of distributions has previously been proposed to improve the complexity of decomposability verification. In this work, we address the problem of generating (optimal) reductions of distributions automatically. A (partial) solution to this problem is provided, which consists of 1) an incremental algorithm for the production of candidate reductions and 2) a reduction validation procedure. In the incremental production stage, backtracking is applied whenever a candidate reduction that cannot be validated is produced. A strengthened substitution-based proof technique is used for reduction validation, while a fixed template of candidate counter examples is used for reduction refutation; put together, they constitute our (partial) solution to the reduction verification problem. In addition, we show that a recursive approach for the generation of (small) reductions is easily supported.

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Experiments with Reduction Finding

Cited by 19 publications

References 15 publications

On Finding a First-Order Sentence Consistent with a Sample of Strings

On Finding a First-Order Sentence Consistent with a Sample of Strings

Towards Bounded Synthesis of Resilient Supervisors

Automatic Generation of Optimal Reductions of Distributions

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