Two-way Transducer Research Articles

Weighted two-way transducers

Weighted two-way transducers over complete commutative semirings are introduced and investigated. Their computed mappings have two-way definable support. Conversely, for every two-way definable relation R there exists a mapping that has support R and is computable by a weighted two-way transducer. The class of all such computed mappings is naturally closed under sum. Finally, both the subclass computed by deterministic weighted two-way transducers and the subclass computed by unambiguous weighted two-way transducers are shown to be closed under composition, pseudo Hadamard product, unambiguous Cauchy product, and unambiguous Kleene iteration.

Regular transducer expressions for regular transformations

Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on infinite words, captured by a deterministic two-way transducer, can be described with a regular transducer expression (RTE ). For infinite words, the two-way transducer uses Muller acceptance and ω-regular look-ahead. RTEs are constructed from constant functions using the combinators if-then-else (deterministic choice), Hadamard product, and unambiguous versions of the Cauchy product, the 2-chained Kleene-iteration and the 2-chained omega-iteration. Our proof works for transformations of both finite and infinite words, extending the result on finite words of Alur et al. in LICS'14.The construction of an RTE associated with a deterministic two-way transducer is guided by a regular expression which is “good” wrt. its transition monoid. “Good” expressions are unambiguous, ensuring the functionality of the output computed. Moreover, in “good” expressions, iterations (Kleene-plus or omega) are restricted to subexpressions corresponding to idempotent elements of the transition monoid. “Good” expressions can be obtained with an unambiguous version of Imre Simon's famous forest factorization theorem.To handle infinite words, we introduce the notion of transition monoids for deterministic two-way Muller transducers with look-ahead, where the look-ahead is captured by some backward deterministic Büchi automaton.This paper is an extended version of [15] presented at LICS'18.

Ultrasonic imaging using air-coupled P(VDF/TrFE) transducers at 2 MHz

A reflection non-contact ultrasonic microscope system working both in amplitude and phase difference modes at 2 MHz has been developed using an air-coupled concave transducer made of piezoelectric polymer films of poly(vinylidene fluoride/trifluoroethylene) [P(VDF/TrFE)]. The transducer is composed of three 95 μm-thick P(VDF/TrFE) films stacked together, each of which is activated electrically in parallel by a driving source. The transducer has a wide aperture angle of 140° and a focal length of 10 mm. The measured two-way transducer insertion loss is 80 dB at 1.83 MHz. Despite 20 dB higher insertion loss than that estimated from Mason’s equivalent circuit, we have obtained clear amplitude acoustic images of a coin with transverse resolution of 150 μm, and clear phase difference acoustic images of the rough surface of a paper currency bill with depth resolution of sub-micrometer. Using two planar transducers of P(VDF/TrFE), we have also successfully measured in through-transmission mode the sound velocity and absorption of a 3 mm-thick silicone-rubber plate. The present study proves that, owing to its low acoustic impedance and flexibility, P(VDF/TrFE) piezoelectric film is very useful for high frequency acoustic imaging in air in the MHz range.

The Equivalence Problem for Single-Valued Two-Way Transducers (on NPDTOL Languages) is Decidable

The equivalence problem for deterministic two-way transducers was a longstanding problem finally shown decidable by E. M. Gurari. We show a generalization of this result, namely that it is decidable whether two single-valued two-way transducers are equivalent on an NPDTOL language. We obtain this result by showing that it is even decidable whether a two-way transducer is single-valued on an NPDTOL language. Our solution is based on the compactness property of the systems of equations over a finitely generated free monoid shown recently by J. Lawrence and M. Albert and also V. S. Guba. This was a longstanding open problem known as the Ehrenfeucht Conjecture. Our approach also shows that for one-way transducers their single-valuedness on a given HDTOL language can be tested, and thus the equivalence of two single-valued one-way transducers on an HDTOL language is decidable, too.Our results imply the decidability of the HDOL and HDTOL sequence equivalence problems, also longstanding open problems solved rece...

The Reciprocal Energy Theorem

This paper gives a simple theorem determining relative transmission efficiencies in a two-way transducer, and showing that the conditions for equal efficiencies of transmission in the two directions are simply those for maximum output and maximum reception of energy. The theorem is then applied to radio communication and a second theorem stated and proved by which the ratio of the transmitting efficiences of any two antenna systems is expressed in terms of their receiving efficiences. The paper closes with a mathematical note on a generalization of Rayleigh's Reciprocal Theorem.