The Alestle - Vol. 54 No. 41 - 02/19/2002

Vol. 54 No. 4

A First-Order Complete Temporal Logic for Structured Context-Free Languages

The problem of model checking procedural programs has fostered much research towards the definition of temporal logics for reasoning on context-free structures. The most notable of such results are temporal logics on Nested Words, such as CaRet and NWTL. Recently, the logic OPTL was introduced, based on the class of Operator Precedence Languages (OPLs), more powerful than Nested Words. We define the new OPL-based logic POTL and prove its FO-completeness. POTL improves on NWTL by enabling the formulation of requirements involving pre/post-conditions, stack inspection, and others in the presence of exception-like constructs. It improves on OPTL too, which instead we show not to be FO-complete; it also allows to express more easily stack inspection and function-local properties. In a companion paper we report a model checking procedure for POTL and experimental results based on a prototype tool developed therefor. For completeness a short summary of this complementary result is provided in this paper too.Comment: Partially supersedes arXiv:1910.0932

Cyclic Operator Precedence Grammars for Parallel Parsing

Operator precedence languages (OPL) enjoy the local parsability property, which essentially means that a code fragment enclosed within a pair of markers -- playing the role of parentheses -- can be compiled with no knowledge of its external context. Such a property has been exploited to build parallel compilers for languages formalized as OPLs. It has been observed, however, that when the syntax trees of the sentences have a linear substructure, its parsing must necessarily proceed sequentially making it impossible to split such a subtree into chunks to be processed in parallel. Such an inconvenience is due to the fact that so far much literature on OPLs has assumed the hypothesis that equality precedence relation cannot be cyclic. This hypothesis was motivated by the need to keep the mathematical notation as simple as possible. We present an enriched version of operator precedence grammars, called cyclic, that allows to use a simplified version of regular expressions in the right hand sides of grammar's rules; for this class of operator precedence grammars the acyclicity hypothesis of the equality precedence relation is no more needed to guarantee the algebraic properties of the generated languages. The expressive power of the cyclic grammars is now fully equivalent to that of other formalisms defining OPLs such as operator precedence automata, monadic second order logic and operator precedence expressions. As a result cyclic operator precedence grammars now produce also unranked syntax trees and sentences with flat unbounded substructures that can be naturally partitioned into chunks suitable for parallel parsing.Comment: 23 pages, 8 figures. arXiv admin note: text overlap with arXiv:2006.0123

The Impact of Precision Tuning on Embedded Systems Performance: A Case Study on Field-Oriented Control

Field Oriented Control (FOC) is an industry-standard strategy for controlling induction motors and other kinds of AC-based motors. This control scheme has a very high arithmetic intensity when implemented digitally - in particular it requires the use of trigonometric functions. This requirement contrasts with the necessity of increasing the control step frequency when required, and the minimization of power consumption in applications where conserving battery life is paramount such as drones. However, it also makes FOC well suited for optimization using precision tuning techniques. Therefore, we exploit the state-of-the-art FixM methodology to optimize a miniapp simulating a typical FOC application by applying precision tuning of trigonometric functions. The FixM approach itself was extended in order to implement additional algorithm choices to enable a trade-off between execution time and code size. With the application of FixM on the miniapp, we achieved a speedup up to 278%, at a cost of an error in the output less than 0.1%

Radiolarian biostratigraphic evidence for a Late Jurassic age of the El Tambor Group ophiolites (Guatemala)

We present a radiolarian biostratigraphic study of the metacherts of the El Tambor Group ophiolites (South Motagua Unit), Guatemala. The ophiolite sequence comprises MOR pillow metabasalts, massive metabasalts, metacherts and micaschists. The age of the studied metacherts is referable to the Late Jurassic (Oxfordian - Kimmeridgian). The radiolarian assemblage described in this paper is the first Jurassic finding in the ophiolitic MOR succession of the Motagua zone and represents a valuable tool to constrain the geodynamic evolution of the Caribbean area. A review of the ages of Jurassic rocks associated with the ophiolites from the Caribbean area is also reported

Correct Approximation of IEEE 754 Floating-Point Arithmetic for Program Verification

Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities, non-numeric objects (NaNs), signed zeroes, denormal numbers, different rounding modes, etc. One possibility to reason about floating-point arithmetic is to model a program computation path by means of a set of ternary constraints of the form z = x op y and use constraint propagation techniques to infer new information on the variables' possible values. In this setting, we define and prove the correctness of algorithms to precisely bound the value of one of the variables x, y or z, starting from the bounds known for the other two. We do this for each of the operations and for each rounding mode defined by the IEEE 754 binary floating-point standard, even in the case the rounding mode in effect is only partially known. This is the first time that such so-called filtering algorithms are defined and their correctness is formally proved. This is an important slab for paving the way to formal verification of programs that use floating-point arithmetics.Comment: 64 pages, 19 figures, 2 table

Recommended number of strides for automatic assessment of gait symmetry and regularity in above-knee amputees by means of accelerometry and autocorrelation analysis

<p>Abstract</p> <p>Background</p> <p>Symmetry and regularity of gait are essential outcomes of gait retraining programs, especially in lower-limb amputees. This study aims presenting an algorithm to automatically compute symmetry and regularity indices, and assessing the minimum number of strides for appropriate evaluation of gait symmetry and regularity through autocorrelation of acceleration signals.</p> <p>Methods</p> <p>Ten transfemoral amputees (AMP) and ten control subjects (CTRL) were studied. Subjects wore an accelerometer and were asked to walk for 70 m at their natural speed (twice). Reference values of step and stride regularity indices (Ad1 and Ad2) were obtained by autocorrelation analysis of the vertical and antero-posterior acceleration signals, excluding initial and final strides. The Ad1 and Ad2 coefficients were then computed at different stages by analyzing increasing portions of the signals (considering both the signals cleaned by initial and final strides, and the whole signals). At each stage, the difference between Ad1 and Ad2 values and the corresponding reference values were compared with the minimum detectable difference, MDD, of the index. If that difference was less than MDD, it was assumed that the portion of signal used in the analysis was of sufficient length to allow reliable estimation of the autocorrelation coefficient.</p> <p>Results</p> <p>All Ad1 and Ad2 indices were lower in AMP than in CTRL (P < 0.0001). Excluding initial and final strides from the analysis, the minimum number of strides needed for reliable computation of step symmetry and stride regularity was about 2.2 and 3.5, respectively. Analyzing the whole signals, the minimum number of strides increased to about 15 and 20, respectively.</p> <p>Conclusions</p> <p>Without the need to identify and eliminate the phases of gait initiation and termination, twenty strides can provide a reasonable amount of information to reliably estimate gait regularity in transfemoral amputees.</p

Gait symmetry and regularity in transfemoral amputees assessed by trunk accelerations

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to evaluate a method based on a single accelerometer for the assessment of gait symmetry and regularity in subjects wearing lower limb prostheses.</p> <p>Methods</p> <p>Ten transfemoral amputees and ten healthy control subjects were studied. For the purpose of this study, subjects wore a triaxial accelerometer on their thorax, and foot insoles. Subjects were asked to walk straight ahead for 70 m at their natural speed, and at a lower and faster speed. Indices of step and stride regularity (Ad1 and Ad2, respectively) were obtained by the autocorrelation coefficients computed from the three acceleration components. Step and stride durations were calculated from the plantar pressure data and were used to compute two reference indices (SI1 and SI2) for step and stride regularity.</p> <p>Results</p> <p>Regression analysis showed that both Ad1 well correlates with SI1 (<it>R</it>²up to 0.74), and Ad2 well correlates with SI2 (<it>R</it>²up to 0.52). A ROC analysis showed that Ad1 and Ad2 has generally a good sensitivity and specificity in classifying amputee's walking trial, as having a normal or a pathologic step or stride regularity as defined by means of the reference indices SI1 and SI2. In particular, the antero-posterior component of Ad1 and the vertical component of Ad2 had a sensitivity of 90.6% and 87.2%, and a specificity of 92.3% and 81.8%, respectively.</p> <p>Conclusions</p> <p>The use of a simple accelerometer, whose components can be analyzed by the autocorrelation function method, is adequate for the assessment of gait symmetry and regularity in transfemoral amputees.</p

Temporal Logic and Model Checking for Operator Precedence Languages

In the last decades much research effort has been devoted to extending the success of model checking from the traditional field of finite state machines and various versions of temporal logics to suitable subclasses of context-free languages and appropriate extensions of temporal logics. To the best of our knowledge such attempts only covered structured languages, i.e. languages whose structure is immediately "visible" in their sentences, such as tree-languages or visibly pushdown ones. In this paper we present a new temporal logic suitable to express and automatically verify properties of operator precedence languages. This "historical" language family has been recently proved to enjoy fundamental algebraic and logic properties that make it suitable for model checking applications yet breaking the barrier of visible-structure languages (in fact the original motivation of its inventor Floyd was just to support efficient parsing, i.e. building the "hidden syntax tree" of language sentences). We prove that our logic is at least as expressive as analogous logics defined for visible pushdown languages yet covering a much more powerful family; we design a procedure that, given a formula in our logic builds an automaton recognizing the sentences satisfying the formula, whose size is at most exponential in the length of the formula.Comment: In Proceedings GandALF 2018, arXiv:1809.0241