scholarly journals A Case Study in Automated Verification Based on Trace Abstractions

1995 ◽  
Vol 2 (54) ◽  
Author(s):  
Nils Klarlund ◽  
Mogens Nielsen ◽  
Kim Sunesen
Keyword(s):  
Reactive Systems ◽  
Main Tool ◽  
Automated Analysis ◽  
Reactive System ◽  
Finite State Automaton ◽  
Symbolic Language ◽  
Temporal Properties ◽  
Finite State ◽  
High Level ◽  
Recursive Data Structures

In [14], we proposed a framework for the automatic verification of reactive<br />systems. Our main tool is a decision procedure, Mona, for Monadic<br />Second-order Logic (M2L) on finite strings. Mona translates a formula in<br />M2L into a finite-state automaton. We show in [14] how traces, i.e. finite<br />executions, and their abstractions can be described behaviorally. These<br />state-less descriptions can be formulated in terms of customized temporal<br />logic operators or idioms.<br />In the present paper, we give a self-contained, introductory account of<br />our method applied to the RPC-memory specification problem of the 1994<br />Dagstuhl Seminar on Specification and Refinement of Reactive Systems.<br />The purely behavioral descriptions that we formulate from the informal<br />specifications are formulas that may span 10 pages or more.<br />Such descriptions are a couple of magnitudes larger than usual temporal<br />logic formulas found in the literature on verification. To securely<br />write these formulas, we introduce Fido [16] as a reactive system description<br />language. Fido is designed as a high-level symbolic language for<br />expressing regular properties about recursive data structures.<br />All of our descriptions have been verified automatically by Mona from<br />M2L formulas generated by Fido.<br />Our work shows that complex behaviors of reactive systems can be<br />formulated and reasoned about without explicit state-based programming.<br />With Fido, we can state temporal properties succinctly while enjoying<br />automated analysis and verification.

scholarly journals On the Expressive Power of Some Extensions of Linear Temporal Logic

2018 ◽  
Vol 25 (5) ◽  
pp. 506-524
Author(s):  
Anton Gnatenko ◽  
Vladimir Zakharov
Keyword(s):  
Temporal Logic ◽  
Reactive Systems ◽  
Expressive Power ◽  
Linear Temporal Logic ◽  
Reactive System ◽  
Formal Specifications ◽  
Control Signals ◽  
Finite State ◽  
Finite State Transducer ◽  
Output Alphabet

One of the most simple models of computation which is suitable for representation of reactive systems behaviour is a finite state transducer which operates over an input alphabet of control signals and an output alphabet of basic actions. The behaviour of such a reactive system displays itself in the correspondence between flows of control signals and compositions of basic actions performed by the system. We believe that the behaviour of this kind requires more suitable and expressive means for formal specifications than the conventionalLT L. In this paper, we define some new (as far as we know) extensionLP-LT Lof Linear Temporal Logic specifically intended for describing the properties of transducers computations. In this extension the temporal operators are parameterized by sets of words (languages) which represent distinguished flows of control signals that impact on a reactive system. Basic predicates in our variant of the temporal logic are also languages in the alphabet of basic actions of a transducer; they represent the expected response of the transducer to the specified environmental influences. In our earlier papers, we considered a model checking problem forLP-LT LandLP-CT Land showed that this problem has effective solutions. The aim of this paper is to estimate the expressive power ofLP-LT Lby comparing it with some well known logics widely used in the computer science for specification of reactive systems behaviour. We discovered that a restricted variant LP-1-LT Lof our logic is more expressive thanLTLand another restricted variantLP-n-LT Lhas the same expressive power as monadic second order logic S1S.

scholarly journals ON SOME PROPERTIES OF TIMED FINITE STATE MACHINES

2020 ◽  
Author(s):  
Evgeniy Maximovich Vinarskii ◽  
◽  
Vladimir Anatolyevoch Zakharov ◽  
Keyword(s):  
Real Time ◽  
Computational Linguistics ◽  
Input Data ◽  
Formal Model ◽  
Reactive Systems ◽  
Real Life ◽  
Reactive System ◽  
Formal Models ◽  
Reactive Behavior ◽  
Finite State

Sequential reactive systems are formal models of programs that interact with the environment by receiving inputs and producing corresponding outputs. Such formal models are widely used in software engineering, computational linguistics, telecommunication, etc. In real life, the behavior of a reactive system depends not only on the flow of input data, but also on the time the input data arrive and the delays that occur when generating responses. To capture these aspects, a timed finite state machine (TFSM) is used as a formal model of a real-time sequential reactive system. However, in most of known previous works, this model was considered in simplified semantics: the responses in the output stream, regardless of their timestamps, follow in the same order in which the corresponding inputs are delivered to the machine. This simplification makes the model easier to analyze and manipulate, but it misses many important aspects of real-time computation. In this paper we study a refined semantics of TFSMs and show how to represent it by means of Labelled Transition Systems. This opens up a possibility to apply traditional formal methods for verifying more subtle properties of real-time reactive behavior which were previously ignored.

scholarly journals Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications

2020 ◽  
Vol 34 (06) ◽  
pp. 9766-9774
Author(s):  
Suguman Bansal ◽  
Yong Li ◽  
Lucas Tabajara ◽  
Moshe Vardi
Keyword(s):  
State Space ◽  
Critical Role ◽  
Hybrid Approach ◽  
Empirical Evaluation ◽  
Finite Horizon ◽  
Reactive System ◽  
State Representation ◽  
Symbolic Representations ◽  
Finite State ◽  
High Level

LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical role in synthesis as well.Therefore, effective resolution of the bottleneck for synthesis requires the conversion to be time and memory performant, and prevent state-space explosion. Current conversion approaches, however, which are based either on explicit-state representation or symbolic-state representation, fail to address these necessities adequately at scale: Explicit-state approaches generate minimal DFA but are slow due to expensive DFA minimization. Symbolic-state representations can be succinct, but due to the lack of DFA minimization they generate such large state spaces that even their symbolic representations cannot compensate for the blow-up.This work proposes a hybrid representation approach for the conversion. Our approach utilizes both explicit and symbolic representations of the state-space, and effectively leverages their complementary strengths. In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck. A comprehensive empirical evaluation on conversion and synthesis benchmarks supports the merits of our hybrid approach.

scholarly journals On the Modeling of Sequential Reactive Systems by Means of Real Time Automata

2020 ◽  
Vol 27 (4) ◽  
pp. 396-411
Author(s):  
Evgeney Maximovich Vinarskii ◽  
Vladimir Anatolyevich Zakharov
Keyword(s):  
Real Time ◽  
Reactive Systems ◽  
Finite State Machines ◽  
Reactive System ◽  
State Machines ◽  
Time Model ◽  
Transition Systems ◽  
Input Signals ◽  
Finite State ◽  
Definition Of

Sequential reactive systems include hardware devices and software programs which operate in continuous interaction with the external environment, from which they receive streams of input signals (data, commands) and in response to them form streams of output signals. Systems of this type include controllers, network switches, program interpreters, system drivers. The behavior of some reactive systems is determined not only by the sequence of values of input signals, but also by the time of their arrival at the inputs of the system and the delays in computing the output signals. These aspects of reactive system computations are taken into account by real-time models of computation which include, in particular, realtime finite state machines (TFSMs). However, in most works where this class of real-time automata is studied a simple variant of TFSM semantics is used: the transduction relation computed by a TFSM is defined so that the elements of an output stream, regardless oftheir timestamps, follow in the same order as the corresponding elements ofthe input stream. This straightforward approach makes the model easier to analyze and manipulate, but it misses many important features of real-time computation. In this paper we study a more realistic semantics of TFSMs and show how to represent it by means of Labeled Transition Systems. The use of the new TFSM model also requires new approaches to the solution of verification problems in the framework of this model. For this purpose, we propose an alternative definition of TFSM computations by means of Labeled Transition Systems and show that the two definitions of semantics for the considered class of real-time finite state machines are in good agreement with each other. The use of TFSM semantics based on Labeled Transition Systems opens up the possibility of adapting well known real-time model checking techniques to the verification ofsequential reactive systems.

scholarly journals Combable functions, quasimorphisms, and the central limit theorem

2009 ◽  
Vol 30 (5) ◽  
pp. 1343-1369 ◽  
Author(s):  
DANNY CALEGARI ◽  
KOJI FUJIWARA
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Word Length ◽  
Hyperbolic Groups ◽  
Finite State Automaton ◽  
List Type ◽  
Generating Sets ◽  
Finite State ◽  
Word Hyperbolic Groups

AbstractA function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite-state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left- and right-invariant word metrics. Examples of bicombable functions on word-hyperbolic groups include:(1)homomorphisms to ℤ;(2)word length with respect to a finite generating set;(3)most known explicit constructions of quasimorphisms (e.g. the Epstein–Fujiwara counting quasimorphisms).We show that bicombable functions on word-hyperbolic groups satisfy acentral limit theorem: if$\overline {\phi }_n$is the value of ϕ on a random element of word lengthn(in a certain sense), there areEandσfor which there is convergence in the sense of distribution$n^{-1/2}(\overline {\phi }_n - nE) \to N(0,\sigma )$, whereN(0,σ) denotes the normal distribution with standard deviationσ. As a corollary, we show that ifS1andS2are any two finite generating sets forG, there is an algebraic numberλ1,2depending onS1andS2such that almost every word of lengthnin theS1metric has word lengthn⋅λ1,2in theS2metric, with error of size$O(\sqrt {n})$.

scholarly journals Method Development and Determination of Chlorinated Polycyclic Aromatic Hydrocarbons in Different Matrices

2021 ◽  
Author(s):  
Carsten Schörnick ◽  
Anja Lüth ◽  
Birgit Wobst ◽  
Wolfgang Rotard
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Method Development ◽  
Automated Analysis ◽  
Proficiency Tests ◽  
Level Of Automation ◽  
Polycyclic Aromatic ◽  
Food And Feed ◽  
Performance Check ◽  
High Level

AbstractThe aim of this study was to develop an analytical method, which separates selected chlorinated polycyclic aromatic hydrocarbons (Cl-PAHs) from fat, and fat-free or vegetable matrices. The method contains extraction-, cleanup-, and quantification steps. Integration of automated analysis actions, as in extraction and cleanup, should enhance the reproducibility, precision, and efficiency of the method. This was confirmed by validation of the overall analytical process. In the end, as a performance check, the developed method was applied on different matrices, e.g., tea, rice, grilled pork, and eel and predator eggs, as a non-food example. An inter-laboratory check was initiated as replacement for the lack of proficiency tests. Due to the high level of automation, both personnel and time effort are very low. In addition, the method is very robust with regard to the variability of the solvent selection and the loss of analytes by evaporation to dryness. It could be demonstrated that the developed method is applicable to different matrices with reproducible and precise results. This applies also to low-fat food and feed.

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