Synthesis of orchestrations of transducers for manufacturing

In this paper, we model manufacturing processes and facilities as transducers (automata with output). The problem of whether a given manufacturing process can be realized by a given set of manufacturing resources can then be stated as an orchestration problem for transducers. We first consider the conceptually simpler case of uni-transducers (transducers with a single input and a single output port), and show that synthesizing orchestrations for uni-transducers is EXPTIME complete. Surprisingly, the complexity remains the same for the more expressive multi-transducer case, where transducers have multiple input and output ports and the orchestration is in charge of dynamically connecting ports during execution

Expressiveness of Streaming String Transducers

Streaming string transducers define (partial) functions from input strings to output strings. A streaming string transducer makes a single pass through the input string and uses a finite set of variables that range over strings from the output alphabet. At every step, the transducer processes an input symbol, and updates all the variables in parallel using assignments whose right-hand-sides are concatenations of output symbols and variables with the restriction that a variable can be used at most once in a right-hand-side expression. It has been shown that streaming string transducers operating on strings over infinite data domains are of interest in algorithmic verification of list-processing programs, as they lead to Pspace decision procedures for checking pre/postconditions and for checking semantic equivalence, for a well-defined class of heap-manipulating programs. In order to understand the theoretical expressiveness of streaming transducers, we focus on streaming transducers processing strings over finite alphabets, given the existence of a robust and well-studied class of ``regular\u27\u27 transductions for this case. Such regular transductions can be defined either by two-way deterministic finite-state transducers, or using a logical MSO-based characterization. Our main result is that the expressiveness of streaming string transducers coincides exactly with this class of regular transductions

LIPIcs

Streaming string transducers [1] define (partial) functions from input strings to output strings. A streaming string transducer makes a single pass through the input string and uses a finite set of variables that range over strings from the output alphabet. At every step, the transducer processes an input symbol, and updates all the variables in parallel using assignments whose right-hand-sides are concatenations of output symbols and variables with the restriction that a variable can be used at most once in a right-hand-side expression. It has been shown that streaming string transducers operating on strings over infinite data domains are of interest in algorithmic verification of list-processing programs, as they lead to PSPACE decision procedures for checking pre/post conditions and for checking semantic equivalence, for a well-defined class of heap-manipulating programs. In order to understand the theoretical expressiveness of streaming transducers, we focus on streaming transducers processing strings over finite alphabets, given the existence of a robust and well-studied class of "regular" transductions for this case. Such regular transductions can be defined either by two-way deterministic finite-state transducers, or using a logical MSO-based characterization. Our main result is that the expressiveness of streaming string transducers coincides exactly with this class of regular transductions

Synthesis of Data Word Transducers

In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata over infinite sequences of signals ($\omega$-words), while implementations are represented as transducers. In the classical setting, the set of signals is assumed to be finite. In this paper, we consider data $\omega$-words instead, i.e., words over an infinite alphabet. In this context, we study specifications and implementations respectively given as automata and transducers extended with a finite set of registers. We consider different instances, depending on whether the specification is nondeterministic, universal or deterministic, and depending on whether the number of registers of the implementation is given or not. In the unbounded setting, we show undecidability for both universal and nondeterministic specifications, while decidability is recovered in the deterministic case. In the bounded setting, undecidability still holds for nondeterministic specifications, but can be recovered by disallowing tests over input data. The generic technique we use to show the latter result allows us to reprove some known result, namely decidability of bounded synthesis for universal specifications

Single transducer for measurement of small displacements or forces

Introduction: One of the limits to characterization of tissues at the microscopic level is the substantial costs associated with the instrumentation required for such investigations. The use of strain gages for displacement or force measurements can be adapted to this microscopic scale provided the gages are incorporated into a transducer consisting of a curved geometry. Materials and Methods: Uniaxial strain gages 13 mm (L) × 6 mm (W) were secured to 0.2-mm thick brass shim stock fabricated to yield a 12.5-mm diameter semicircle with mounting tabs on either end. The terminal ends of the strain gage mounting pads were connected to an adjustable strain gage amplifier with adjustable gain and offset. For displacement calibration, the transducer was secured to the jaws of a digital caliper. Caliper displacement was set to ±0.25 mm increments from 0 to a maximum of ±1.5 mm. In this configuration, positive represents tension. Amplifier Gains were set to 500, 1000, and 5000 to observe nonlinearity. For each of three displacement calibration runs, output voltage from the transducer was recorded at each distance with the mean output at absolute distances averaged across each of three runs for each of six transducers. Using the same transducers, a mass balance was used to identify the unique individual mass associated with a total of 10 masses to within ±10 μg. The masses were sequentially secured to the transducer and the respective output voltage recorded. Amplifier Gains were set to 500, 1000 and 5000. For each of three force calibration runs, output voltage from the transducer was recorded with respect to the force generated by the suspended masses. The mean output across each of three runs for each of six transducers was subjected to linear regression. Results and Discussion: All transducers displayed good linearity when calibrated for displacement with regression R2 values of 0.9994, 0.9967, and 0.9941 for amplifier gains of 500, 1000, and 5000, respectively. Further, in displacement mode, the transducers provided a mean output of 0.66, 1.01, and 3.86 V/mm at amplifier gains of 500, 1000, and 5000, respectively. In force mode, regression R2 in excess of 0.9995 were observed over all amplifier gain settings examined. When employed as force transducers, the devices provided mean outputs of 0.60, 1.15, and 5.85 V/N at amplifier gains of 500, 1000, and 5000, respectively. The response of these devices to either applied displacement or force permits the use of a single device type to be used as either a displacement or force transducer. The electrical output in either mode at modest amplification gains of 5000 combined with excellent linearity affords the use of these devices for studies where characterization of tissues requires mN and μm level resolution. Conclusions: A transducer employing a strain gage had been configured so as to function as either a displacement or force measuring instrument. The resulting device displays high linearity and electrical output even at modest amplifier gains

The complexity of two finite-state models, optimizing transducers and counting automata

An optimizing finite-state transducer is a nondeterministic finite-state transducer in which states are either maximizing or minimizing. In a given state, the optimal output is the maximum or minimum--over all possible transitions--of the transition output concatenated with the optimal output of the resulting state. The ranges of optimizing finite-state transducers form a class in NL which includes a hierarchy based on the number of alternations of maximizing and minimizing states in a computation. The inequivalence problem--whether or not two transducers compute different functions, and the range inequivalence problem are shown to be undecidable. Some other problems associated with this model are shown to be complete for NL and NP;A counting finite-state automaton is a nondeterministic finite-state automaton which, on an input over its input alphabet, (magically) writes in binary the number of accepting computations on the input. We examine the complexity of computing the counting function of an NFA, and the complexity of recognizing its range as a set of binary strings. We also consider the pumping behavior of counting finite-state automata. The class of functions computed by counting NFAs (1) includes a class of functions computed by deterministic finite-state transducers; (2) is contained in the class of functions computed by polynomially time- and linearly space-bounded Turing transducers; (3) includes a function whose range is the composite numbers

Regular Combinators for String Transformations

We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way finite-state transducers, (one-way) cost register automata, and MSO-definable graph transformations. In this paper, we give an algebraic and machine-independent characterization of this class analogous to the definition of regular languages by regular expressions. When the monoid is commutative, we prove that every regular function can be constructed from constant functions using the combinators of choice, split sum, and iterated sum, that are analogs of union, concatenation, and Kleene-*, respectively, but enforce unique (or unambiguous) parsing. Our main result is for the general case of non-commutative monoids, which is of particular interest for capturing regular string-to-string transformations for document processing. We prove that the following additional combinators suffice for constructing all regular functions: (1) the left-additive versions of split sum and iterated sum, which allow transformations such as string reversal; (2) sum of functions, which allows transformations such as copying of strings; and (3) function composition, or alternatively, a new concept of chained sum, which allows output values from adjacent blocks to mix.Comment: This is the full version, with omitted proofs and constructions, of the conference paper currently in submissio

Lipschitz Robustness of Finite-state Transducers

We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions. We show that K-robustness is undecidable even for deterministic transducers. We identify a class of functional transducers, which admits a polynomial time automata-theoretic decision procedure for K-robustness. This class includes Mealy machines and functional letter-to-letter transducers. We also study K-robustness of nondeterministic transducers. Since a nondeterministic transducer generates a set of output words for each input word, we quantify output perturbation using set-similarity functions. We show that K-robustness of nondeterministic transducers is undecidable, even for letter-to-letter transducers. We identify a class of set-similarity functions which admit decidable K-robustness of letter-to-letter transducers.Comment: In FSTTCS 201