Nondeterministic Finite-state Transducers Research Articles

Language Recovery in Discrete-Event Systems against Sensor Deception Attacks

Cyber-physical systems are characterized by the intrinsic combination of software and physical components that usually include (wired and wireless) communication devices, sensors, actuators, and control processing units. Some wireless devices communicate over insecure channels, rendering cyber-physical systems at risk of malicious attacks that might lead to catastrophic damage. This paper touches upon the problem of sensor deception attacks in supervisory control of discrete-event systems, where an attacker can insert, delete, or replace sensor readings to mislead the supervisor and induce system damage. We model potential attacks using nondeterministic finite-state transducers and then introduce a new defence strategy that utilizes insertion functions. Insertion functions are a type of monitoring interface that alters the system’s behaviour by adding extra observable events. Finally, we construct a nondeterministic finite-state transducer called a supervisor filter that recovers the original language generated by the plant by handling the altered language. The insertion function and the supervisor filter cooperate to control the system and confuse the intruder without confusing the supervisor.

Multi-Sequential Word Relations

Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A multi-sequential relation is a rational relation which is equal to a finite union of (graphs) of partial sequential functions, i.e. functions realised by input-deterministic transducers. The particular case of multi-sequential functions was studied by Choffrut and Schützenberger who proved that given a rational function (as a transducer), it is decidable whether it is multi-sequential. Their procedure is based on an effective characterisation of unambiguous transducers that do not define multi-sequential functions, that we call the fork property. In this paper, we show that the fork property also characterises the class of transducers that do not define multi-sequential relations. Moreover, we prove that the fork property can be decided in PTime. This leads to a PTime procedure which, given a transducer, decides whether it defines a multi-sequential relation.

Normality and two-way automata

We prove that two-way transducers (both deterministic and non-deterministic) cannot compress normal numbers. To achieve this, we first show that it is possible to generalize compressibility from one-way transducers to two-way transducers. These results extend a known result: normal infinite words are exactly those that cannot be compressed by lossless finite-state transducers, and, more generally, by bounded-to-one non-deterministic finite-state transducers. We also argue that such a generalization cannot be extended to two-way transducers with unbounded memory, even in the simple form of a single counter.

Autopoietic automata: Complexity issues in offspring-producing evolving processes

We introduce a new formal computational model designed for studying the information transfer among the generations of offspring-producing evolving machines — so-called autopoietic automata. These can be seen as nondeterministic finite state transducers whose “program” can become a subject of their own processing. An autopoietic automaton can algorithmically generate an offspring controlled by a program which is a modification of its parent’s program. Autopoietic automata offer a neat framework for investigating computational and complexity issues in the evolutionary self-reproducing processes. We show that the computational power of lineages of autopoietic automata is equal to that of an interactive nondeterministic Turing machine. We also prove that there exists an autopoietic automaton giving rise to an unlimited evolution, provided that suitable inputs are delivered to individual automata. However, the problem of sustainable evolution, asking whether for an arbitrary autopoietic automaton and arbitrary inputs there is an infinite lineage of its offspring, is undecidable.

Parallel parsing on a one-way linear array of finite-state machines

Efficient parallel algorithms for some parsing problems are presented. These problems include the parsing of linear context-free languages, languages accepted by nondeterministic one-counter automata, and transductions defined by a special class of two-tape nondeterministic finite-state transducers. The model of parallel computation is a one-way linear array of identical finite-state machines. The data movement in the array is one-way, from left to right. For inputs of length n, the array uses n nodes. Our algorithms can actually produce a parse, i.e. a sequence of rules (moves) that generates (accepts) an input, in linear time. When only a no/yes answer is required, the parsing problem becomes a recognition problem. The best serial (RAM) algorithms for the corresponding recognition problems take O( n 2/log 2 n) time and space. Previous parallel algorithms for the recognition problems run in linear time on a one-way linear array of finite-state machines.

Absolutely parallel grammars and two-way finite-state transducers

Absolutely parallel grammars are defined, and it, is shown that the family of languages generated is equal to the family of languages generated by two-way deterministic finite-state transducers (abbreviated 2ft). Furthermore it is shown that this family forms a full AFL closed under substitution. It is shown that the family of languages generated by two-way nondeterministic finite-state transducers is equal to the family of checking automata languages and that it properly contains the family of languages generated by 2ft.