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 the Model Checking Problem for Some Extension of CTL*

2020 ◽  
Vol 27 (4) ◽  
pp. 428-441
Author(s):  
Anton Romanovich Gnatenko ◽  
Vladimir Anatolyevich Zakharov
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Reactive Systems ◽  
Expressive Power ◽  
Binary Relations ◽  
Temporal Logics ◽  
Distinctive Features ◽  
Verification Problem ◽  
Finite State ◽  
Infinite Sequences

Sequential reactive systems include programs and devices that work with two streams of data and convert input streams of data into output streams. Such information processing systems include controllers, device drivers, computer interpreters. The result of the operation of such computing systems are infinite sequences of pairs of events of the request-response type, and, therefore, finite transducers are most often used as formal models for them. The behavior of transducers is represented by binary relations on infinite sequences, and so, traditional applied temporal logics (like HML, LTL, CTL, mu-calculus) are poorly suited as specification languages, since omega-languages, not binary relations on omega-words are used for interpretation of their formulae. To provide temporal logics with the ability to define properties of transformations that characterize the behavior ofreactive systems, we introduced new extensions ofthese logics, which have two distinctive features: 1) temporal operators are parameterized, and languages in the input alphabet oftransducers are used as parameters; 2) languages in the output alphabet oftransducers are used as basic predicates. Previously, we studied the expressive power ofnew extensions Reg-LTL and Reg-CTL ofthe well-known temporal logics oflinear and branching time LTL and CTL, in which it was allowed to use only regular languages for parameterization of temporal operators and basic predicates. We discovered that such a parameterization increases the expressive capabilities oftemporal logic, but preserves the decidability of the model checking problem. For the logics mentioned above, we have developed algorithms for the verification of finite transducers. At the next stage of our research on the new extensions of temporal logic designed for the specification and verification of sequential reactive systems, we studied the verification problem for these systems using the temporal logic Reg-CTL*, which is an extension ofthe Generalized Computational Tree Logics CTL*. In this paper we present an algorithm for checking the satisfiability of Reg-CTL* formulae on models of finite state transducers and show that this problem belongs to the complexity class ExpSpace.

scholarly journals USING AN EXTENSIONS OF CTL* FOR SPECIFICATION AND VERIFICATION OF SEQUENTIAL REACTIVE SYSTEMS

2020 ◽  
Author(s):  
Anton Romanovich Gnatenko ◽  
◽  
Vladimir Anatolyevoch Zakharov ◽  
Keyword(s):  
Model Checking ◽  
Formal Model ◽  
Reactive Systems ◽  
Expressive Power ◽  
Binary Relations ◽  
Temporal Logics ◽  
Finite State Transducers ◽  
Control Signals ◽  
Data Control ◽  
Finite State

Sequential reactive systems such as controllers, device drivers, computer interpreters operate with two data streams and transform input streams of data (control signals, instructions) into output streams of control signals (instructions, data). Finite state transducers are widely used as an adequate formal model for information processing systems of this kind. Since runs of transducers develop over time, temporal logics, obviously, could be used as both simple and expressive formalism for specifying the behavior of sequential reactive systems. However, the conventional applied temporal logics (LTL, CTL) do not suit this purpose well, since their formulae are interpreted over omega-languages, whereas the behavior of transducers are represented by binary relations on infinite sequences, i.e. omega-transductions. To provide temporal logic with the ability to take into account this general feature of the behavior of reactive systems, we introduced new extensions of this logic. Two distinguished features characterize these extension: 1) temporal operators are parameterized by sets of streams (languages) admissible for input, and 2) sets (languages) of expected output streams are used as basic predicates. In the previous series of works we studied the expressive power and the model checking problem for Reg-LTL and Reg-CTL which are such extensions of LTL and CTL where the languages mentioned above are regular ones. We discovered that such an extension of temporal logics increases their expressive capability though retains the decidability of the model checking problem. Our next step in the systematic study of expressive and algorithmic properties of new extensions temporal logics is the analysis of the model checking problem for finite state transducers against Reg-CTL* formulae. In this paper we develop a model checking algorithm for Reg-CTL* and show that this problem is in ExpSpace.

FINITE STATE PROCESSES, Z-TEMPORAL LOGIC AND THE MONADIC THEORY OF THE INTEGERS

1992 ◽  
Vol 03 (03) ◽  
pp. 233-244 ◽  
Author(s):  
A. SAOUDI ◽  
D.E. MULLER ◽  
P.E. SCHUPP
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Second Order ◽  
Regular Languages ◽  
Infinite Words ◽  
First Order ◽  
Monadic Theory ◽  
Finite State ◽  
Temporal Formula

We introduce four classes of Z-regular grammars for generating bi-infinite words (i.e. Z-words) and prove that they generate exactly Z-regular languages. We extend the second order monadic theory of one successor to the set of the integers (i.e. Z) and give some characterizations of this theory in terms of Z-regular grammars and Z-regular languages. We prove that this theory is decidable and equivalent to the weak theory. We also extend the linear temporal logic to Z-temporal logic and then prove that each Z-temporal formula is equivalent to a first order monadic formula. We prove that the correctness problem for finite state processes is decidable.

Mirror, mirror in my hand: a duality between specifications and models of process behaviour

1996 ◽  
Vol 6 (4) ◽  
pp. 353-373 ◽  
Author(s):  
J. L. Fiadeiro ◽  
J. F. Costa
Keyword(s):  
Temporal Logic ◽  
Structural Property ◽  
Reactive Systems ◽  
Expressive Power ◽  
Seminal Paper ◽  
Process Specification ◽  
Temporal Specifications ◽  
Mirror Mirror

SummarySince Pnueli’s seminal paper in 1977, Temporal Logic has been used as a formalism for specifying and verifying the correctness of reactive systems. In this paper, we show that, besides its expressive power, Temporal Logic enjoys a very strong structural property: it is categorical on processes. That is, we show how temporal specifications (as theories) can be embedded in categories of process behaviour, and out of this adjunction we build an institution that is categorical in the sense of Meseguer. This characterisation means that temporal logic is, in a sense, ‘sound and complete’ with respect to process specification and interconnection techniques.

scholarly journals On the Satisfiability and Model Checking for one Parameterized Extension of Linear-time Temporal Logic

2021 ◽  
Vol 28 (4) ◽  
pp. 356-371
Author(s):  
Anton Romanovich Gnatenko ◽  
Vladimir Anatolyevich Zakharov
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Linear Time ◽  
Complete Solution ◽  
Reactive Systems ◽  
Expressive Power ◽  
Regular Languages ◽  
Specification Languages ◽  
Temporal Logics ◽  
Emptiness Problem

Sequential reactive systems are computer programs or hardware devices which process the flows of input data or control signals and output the streams of instructions or responses. When designing such systems one needs formal specification languages capable of expressing the relationships between the input and output flows. Previously, we introduced a family of such specification languages based on temporal logics $LTL$, $CTL$ and $CTL^*$ combined with regular languages. A characteristic feature of these new extensions of conventional temporal logics is that temporal operators and basic predicates are parameterized by regular languages. In our early papers, we estimated the expressive power of the new temporal logic $Reg$-$LTL$ and introduced a model checking algorithm for $Reg$-$LTL$, $Reg$-$CTL$, and $Reg$-$CTL^*$. The main issue which still remains unclear is the complexity of decision problems for these logics. In the paper, we give a complete solution to satisfiability checking and model checking problems for $Reg$-$LTL$ and prove that both problems are Pspace-complete. The computational hardness of the problems under consideration is easily proved by reducing to them the intersection emptyness problem for the families of regular languages. The main result of the paper is an algorithm for reducing the satisfiability of checking $Reg$-$LTL$ formulas to the emptiness problem for Buchi automata of relatively small size and a description of a technique that allows one to check the emptiness of the obtained automata within space polynomial of the size of input formulas.

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 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.

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