Synthesis for Probabilistic Environments

Schewe, Sven

doi:10.1007/11901914_20

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…A run tree is accepted by the ABS T C if colour 2 is seen infinitely often on all infinite paths. Similar constructions can be found in [13,Section 3].…”

Section: Detailed Constructionsmentioning

confidence: 53%

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Deciding What is Good-for-MDPs

Schewe¹,

Tang²,

Tansholpan³

2022

Preprint

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Nondeterministic Good-for-MDP (GFM) automata are for MDP model checking and reinforcement learning what good-for-games automata are for synthesis: a more compact alternative to deterministic automata that displays nondeterminism, but only so much that it can be resolved locally, such that a syntactic product can be analysed. GFM has recently been introduced as a property for reinforcement learning, where the simpler Büchi acceptance conditions it allows to use is key. However, while there are classic and novel techniques to obtain automata that are GFM, there has not been a decision procedure for checking whether or not an automaton is GFM. We show that GFM-ness is decidable and provide an EXPTIME decision procedure as well as a PSPACE-hardness proof. ACM Subject ClassificationTheory of computation → Automata over infinite objects; Mathematics of computing → Markov processes

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“…A run tree is accepted by the ABS T C if colour 2 is seen infinitely often on all infinite paths. Similar constructions can be found in [13,Section 3].…”

Section: Detailed Constructionsmentioning

confidence: 53%

“…As a result, we can search for the (regular) tree that stems from the unravelling of a Markov chain, while disregarding probabilities. This observation has been used in the synthesis of probabilistic systems before [13]. The set Υ could then, for example, be chosen to be the set of states of the unravelled finite MDP; this would not normally be a full tree.…”

mentioning

confidence: 99%

Deciding What is Good-for-MDPs

Schewe¹,

Tang²,

Tansholpan³

2022

Preprint

Self Cite

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“…Proof. We prove the lemma along the steps of [20]. Let A be defined over the alphabet 2 AP for a set of atomic proposition AP.…”

Section: Density Of ω-Regular Propertiesmentioning

confidence: 99%

The Density of Linear-Time Properties

Finkbeiner

Torfah

2017

Automated Technology for Verification and Analysis

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Finding models for linear-time properties is a central problem in verification and planning. We study the distribution of lineartime models by investigating the density of linear-time properties over the space of ultimately periodic words. The density of a property over a bound n is the ratio of the number of lasso-shaped words of length n, that satisfy the property, to the total number of lasso-shaped words of length n. We investigate the problem of computing the density for both linear-time properties in general and for the important special case of ωregular properties. For general linear-time properties, the density is not necessarily convergent and can oscillates indefinitely for certain properties. However, we show that the oscillation is bounded by the growth of the sets of bad-and good-prefix of the property. For ω-regular properties, we show that the density is always convergent and provide a general algorithm for computing the density of ω-regular properties as well as more specialized algorithms for certain sub-classes and their combinations.

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“…Since the question of whether a given composition satisfies α boils down to whether its composer has a choice function that has an odd rank, we find it useful to characterize regular trees that correspond to choice functions having a particular rank (see [19] for related results). First, we inductively define the set of marked nodes of a Γ-labeled D-tree as follows: the root is always marked, and a node y · i, where i ∈ D and y ∈ D * , is marked if y is marked and i ∈ X, where (X, j, M ) is the label on y · i. Lemma 4.10.…”

Section: Stagementioning

confidence: 99%

Synthesis from Probabilistic Components

Nain

Lustig

Vardi

2014

Logical Methods in Computer Science

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Abstract. Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms, it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course, rarely happens in real life, where almost every non-trivial commercial software system relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. Recently, Lustig and Vardi introduced dataflow and control-flow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while controlflow synthesis is decidable. In this work, we consider the problem of control-flow synthesis from libraries of probabilistic components. We show that this more general problem is also decidable.

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Synthesis for Probabilistic Environments

Cited by 4 publications

References 16 publications

Deciding What is Good-for-MDPs

Deciding What is Good-for-MDPs

The Density of Linear-Time Properties

Synthesis from Probabilistic Components

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