Quantitative Languages Defined by Functional Automata

Filiot, Emmanuel; Gentilini, Raffaella; Raskin, Jean-François

doi:10.1007/978-3-642-32940-1_11

Cited by 21 publications

(24 citation statements)

References 25 publications

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“…We show that many of the properties from the literature, including all the properties mentioned before, can be expressed in these logics. As a consequence, we show that most of the PTIME upper-bounds obtained for deciding subclasses of finite automata in [25,2], of transducers in [6,14,24,22,16,7,5,18,8] and sum-automata in [11,10,8,3], can be directly obtained by expressing in our logics the structural patterns given in these papers, which characterise these subclasses.…”

Section: Contributionsmentioning

confidence: 80%

“…We refer the reader to the mentioned references for the formal definitions. The class of functional sumautomata [11] are those such that all accepting paths associated with a given word return the same value. The classes of k-valued [10] and k-sequential sum-automata [8] are defined similarly as for transducers.…”

Section: A Pattern Logic For Sum-automatamentioning

confidence: 99%

“…We have already shown in the introduction that functionality [11] and more generally k-valuedness [10] are expressible in PL = Sum . The twinning property [11,1] is as well expressible in PL = Sum , just by replacing in the formula expressing it for transducers (proof of Thm. 5) the atom SDel = (v 1 , v ′ 1 , v 2 , v ′ 2 ) by v ′ 1 = v ′ 2 .…”

Section: A Pattern Logic For Sum-automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…automata with outputs in (Z, +, 0), which defines relations from words to Z. Properties such as functionality, determinisability, and k-valuedness (for a fixed k) are decidable in PTIME for sum-automata [11,10].In our experience, it is quite often the case that deciding a subclass goes in two steps: (1) define a characterisation of the subclass through a "simple" pattern, (2) show how to decide the existence of a such a pattern. For instance, the determinisable transducers have been characterised via the so called twinning property [6,24,4], which, said briefly, asks that the output words produced by any two different paths on input words of the form uv n cannot differ unboundedly when n grows, with a suitable definition of "differ".…”

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confidence: 99%

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A Pattern Logic for Automata with Outputs

Filiot

Mazzocchi

Raskin

2018

Developments in Language Theory

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We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient conditions on the predicates under which the model-checking problem is decidable. We then consider three particular automata models (finite automata, transducers and automata weighted by integers -sum-automata -) and instantiate the generic logic for each of them. We give tight complexity results for the three logics and the model-checking problem, depending on whether the formula is fixed or not. We study the expressiveness of our logics by expressing classical structural patterns characterising for instance finite ambiguity and polynomial ambiguity in the case of finite automata, determinisability and finite-valuedness in the case of transducers and sum-automata. Consequently to our complexity results, we directly obtain that these classical properties can be decided in PTIME. IntroductionMotivations An important aspect of automata theory is the definition of automata subclasses with particular properties, of algorithmic interest for instance. As an example, the inclusion problem for non-deterministic finite automata is PSPACE-C but becomes PTIME if the automata are k-ambiguous for a fixed k [21].By automata theory, we mean automata in the general sense of finite state machines processing finite words. This includes what we call automata with outputs, which may also produce output values in a fixed monoid M = (D, ⊕, 0). In such an automaton, the transitions are extended with an (output) value in D, and the value of an accepting path is the sum (for ⊕) of all the values occurring along its transitions. Automata over finite words in Λ * and with outputs in M define subsets of Λ * × D as follows: to any input word w ∈ Λ * , we associate the set of values of all the accepting paths on w. For example, transducers are automata with outputs in a free monoid: they process input words and produce output words and therefore define binary relations of finite words [15].The many decidability properties of finite automata do not carry over to transducers, and many restrictions have been defined in the literature to recover decidability, or just to define subclasses relevant to particular applications. The inclusion problem for transducer is undecidable [13], but decidable for finitevalued transducers [23]. Another well-known subclass is that of the determinisable transducers [5], defining sequential functions of words. Finite-valuedness and determinisability are two properties decidable in PTIME, i.e., it is decidable in PTIME, given a transducer, whether it is finite-valued (resp. determinisable). As a second example of automata with outputs, we also consider sum-automata, i.e. automata with outputs in (Z, +, 0), which defines relations from words to Z. Properties such as functionality, determinisability, and k-valuedness (for a fixed k) are decidable in PTIME for sum-automata [11,10].In our e...

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Section: Contributionsmentioning

confidence: 80%

Section: A Pattern Logic For Sum-automatamentioning

confidence: 99%

Section: A Pattern Logic For Sum-automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A Pattern Logic for Automata with Outputs

Filiot

Mazzocchi

Raskin

2018

Developments in Language Theory

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Safety and Co-safety Comparator Automata for Discounted-Sum Inclusion

Bansal

Vardi

2019

Computer Aided Verification

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Discounted-sum inclusion (DS-inclusion, in short) formalizes the goal of comparing quantitative dimensions of systems such as cost, resource consumption, and the like, when the mode of aggregation for the quantitative dimension is discounted-sum aggregation. Discounted-sum comparator automata, or DS-comparators in short, are Büchi automata that read two infinite sequences of weights synchronously and relate their discounted-sum. Recent empirical investigations have shown that while DS-comparators enable competitive algorithms for DS-inclusion, they still suffer from the scalability bottleneck of Büchi operations. Motivated by the connections between discounted-sum and Büchi automata, this paper undertakes an investigation of language-theoretic properties of DS-comparators in order to mitigate the challenges of Büchi DS-comparators to achieve improved scalability of DS-inclusion. Our investigation uncovers that DS-comparators possess safety and co-safety language-theoretic properties. As a result, they enable reductions based on subset construction-based methods as opposed to higher complexity Büchi complementation, yielding tighter worst-case complexity and improved empirical scalability for DS-inclusion.

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Qualitative Controller Synthesis for Consumption Markov Decision Processes

Blahoudek

Brázdil

Novotný

et al. 2020

Computer Aided Verification

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Consumption Markov Decision Processes (CMDPs) are probabilistic decision-making models of resource-constrained systems. In a CMDP, the controller possesses a certain amount of a critical resource, such as electric power. Each action of the controller can consume some amount of the resource. Resource replenishment is only possible in special reload states, in which the resource level can be reloaded up to the full capacity of the system. The task of the controller is to prevent resource exhaustion, i.e. ensure that the available amount of the resource stays non-negative, while ensuring an additional linear-time property. We study the complexity of strategy synthesis in consumption MDPs with almost-sure Büchi objectives. We show that the problem can be solved in polynomial time. We implement our algorithm and show that it can efficiently solve CMDPs modelling real-world scenarios.

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Quantitative Languages Defined by Functional Automata

Cited by 21 publications

References 25 publications

A Pattern Logic for Automata with Outputs

A Pattern Logic for Automata with Outputs

Safety and Co-safety Comparator Automata for Discounted-Sum Inclusion

Qualitative Controller Synthesis for Consumption Markov Decision Processes

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