Synthesis of a nondeterministic automaton from its logical specification. I

1995 ◽  
Vol 31 (5) ◽  
pp. 641-649 ◽  
Author(s):  
A. N. Chebotarev
Keyword(s):  
Nondeterministic Automaton ◽  
Logical Specification

Synthesis of a nondeterministic automaton from its logical specification. II

1995 ◽  
Vol 31 (6) ◽  
pp. 793-801
Author(s):  
A. N. Chebotarev
Keyword(s):  
Nondeterministic Automaton ◽  
Logical Specification

Minimal Size of Counters for (Real-Time) Multicounter Automata

2021 ◽  
Vol 181 (2-3) ◽  
pp. 99-127
Author(s):  
Viliam Geffert ◽  
Zuzana Bednárová
Keyword(s):  
Finite Number ◽  
Real Time ◽  
The Other ◽  
Binary Representation ◽  
Minimal Size ◽  
Nondeterministic Automaton ◽  
Other Hand ◽  
Weak Space ◽  
Fixed Constant

We show that, for automata using a finite number of counters, the minimal space that is required for accepting a nonregular language is (log n)ɛ. This is required for weak space bounds on the size of their counters, for real-time and one-way, and for nondeterministic and alternating versions of these automata. The same holds for two-way automata, independent of whether they work with strong or weak space bounds, and of whether they are deterministic, nondeterministic, or alternating. (Here ɛ denotes an arbitrarily small—but fixed—constant; the “space” refers to the values stored in the counters, rather than to the lengths of their binary representation.) On the other hand, we show that the minimal space required for accepting a nonregular language is nɛ for multicounter automata with strong space bounds, both for real-time and one-way versions, independent of whether they are deterministic, nondeterministic, or alternating, and also for real-time and one-way deterministic multicounter automata with weak space bounds. All these bounds are optimal both for unary and general nonregular languages. However, for automata equipped with only one counter, it was known that one-way nondeterministic automata cannot recognize any unary nonregular languages at all, even if the size of the counter is not restricted, while, with weak space bound log n, we present a real-time nondeterministic automaton recognizing a binary nonregular language here.

MINIMIZATION OF PLANAR DIRECTED ACYCLIC GRAPH ALGEBRAS

2013 ◽  
Vol 24 (04) ◽  
pp. 519-531
Author(s):  
ANTONIOS KALAMPAKAS ◽  
OLYMPIA LOUSCOU-BOZAPALIDOU
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Graph Algebras ◽  
Minimization Method ◽  
Nondeterministic Automaton ◽  
Acyclic Graph ◽  
Acyclic Graphs

We introduce planar directed acyclic graph algebras and present an explicit minimization method. The minimal simulation of a nondeterministic automaton on planar directed acyclic graphs is constructed.

scholarly journals Embedding time granularity in a logical specification language for synchronous real-time systems

1993 ◽  
Vol 20 (1-2) ◽  
pp. 141-171 ◽  
Author(s):  
E. Ciapessoni ◽  
E. Corsetti ◽  
A. Montanari ◽  
P. San Pietro
Keyword(s):  
Real Time ◽  
Specification Language ◽  
Real Time Systems ◽  
Logical Specification ◽  
Time Systems

scholarly journals Automatic Synthesis of Real Time Systems

1994 ◽  
Vol 1 (45) ◽  
Author(s):  
Jørgen H. Andersen
Keyword(s):  
Real Time ◽  
Model Construction ◽  
Real Time Systems ◽  
Automatic Synthesis ◽  
Prototype Implementation ◽  
Construction Problem ◽  
Verification Tool ◽  
Logical Specification ◽  
Direct Model ◽  
Time Systems

This paper presents a method for automatically constructing real time systems directly from their specifications. The model-construction problem is considered for implicit specifications of the form: <br />(A_1 | . . . | A_n | X) sat S <br /> where S is a real time (logical) specification, A_1, ... , A_n are given (regular) timed agents and the problem is to decide whether there exists (and if possible exhibit) a real time agent X which when put in parallel with A_1, ..., A_n will yield a network satisfying S. The method presented proceeds in two steps: first, the implicit specification of X is transformed into an equivalent direct specification of X; second, a model for this direct specification is constructed (if possible) using a direct model construction algorithm. A prototype implementation of our method has been added to the real time verification tool EPSILON.

scholarly journals Investigation of observability property of controlled binary dynamical systems: a logical approach

2021 ◽  
Author(s):  
G.A. Oparin ◽  
V.G. Bogdanova ◽  
A.A. Pashinin
Keyword(s):  
Dynamical Systems ◽  
Binary System ◽  
System Dynamics ◽  
Boolean Model ◽  
Boolean Formula ◽  
Formal Definition ◽  
Applied Logic ◽  
Quantified Boolean Formula ◽  
Logical Specification ◽  
Definition Of

The property of observability of controlled binary dynamical systems is investigated. A formal definition of the property is given in the language of applied logic of predicates with bounded quantifiers of existence and universality. A Boolean model of the property is built in the form of a quantified Boolean formula accordingly to the Boolean constraints method developed by the authors. This formula satisfies both the logical specification of the property and the equations of the binary system dynamics. Aspects of the proposed approach implementation for the study of the observability property are considered. The technology of checking the feasibility of the property using an applied microservice package is demonstrated in several examples.

scholarly journals MonkeyDB: effectively testing correctness under weak isolation levels

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-27
Author(s):  
Ranadeep Biswas ◽  
Diptanshu Kakwani ◽  
Jyothi Vedurada ◽  
Constantin Enea ◽  
Akash Lal
Keyword(s):  
Social Networking ◽  
Large Scale ◽  
Storage Systems ◽  
Storage System ◽  
Trade Off ◽  
Read Operation ◽  
A Value ◽  
Logical Specification ◽  
Good Coverage

Modern applications, such as social networking systems and e-commerce platforms are centered around using large-scale storage systems for storing and retrieving data. In the presence of concurrent accesses, these storage systems trade off isolation for performance. The weaker the isolation level, the more behaviors a storage system is allowed to exhibit and it is up to the developer to ensure that their application can tolerate those behaviors. However, these weak behaviors only occur rarely in practice and outside the control of the application, making it difficult for developers to test the robustness of their code against weak isolation levels. This paper presents MonkeyDB, a mock storage system for testing storage-backed applications. MonkeyDB supports a key-value interface as well as SQL queries under multiple isolation levels. It uses a logical specification of the isolation level to compute, on a read operation, the set of all possible return values. MonkeyDB then returns a value randomly from this set. We show that MonkeyDB provides good coverage of weak behaviors, which is complete in the limit. We test a variety of applications for assertions that fail only under weak isolation. MonkeyDB is able to break each of those assertions in a small number of attempts.

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