Transition Function Complexity of Finite Automata

Author(s):  
Māris Valdats
2003 ◽  
Vol 14 (04) ◽  
pp. 605-624 ◽  
Author(s):  
Constantinos Bartzis ◽  
Tevfik Bultan

In this paper we discuss efficient symbolic representations for infinite-state systems specified using linear arithmetic constraints. We give algorithms for constructing finite automata which represent integer sets that satisfy linear constraints. These automata can represent either signed or unsigned integers and have a lower number of states compared to other similar approaches. We present efficient storage techniques for the transition function of the automata and extend the construction algorithms to formulas on both boolean and integer variables. We also derive conditions which guarantee that the pre-condition computations used in symbolic verification algorithms do not cause an exponential increase in the automata size. We experimentally compare different symbolic representations by using them to verify non-trivial concurrent systems. Experimental results show that the symbolic representations based on our construction algorithms outperform the polyhedral representation used in Omega Library, and the automata representation used in LASH.


Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 813
Author(s):  
José M. Sempere

In this work, we analyze the computational power of Watson-Crick finite automata (WKFA) if some restrictions over the transition function in the model are imposed. We consider that the restrictions imposed refer to the maximum length difference between the two input strands which is called the delay. We prove that the language class accepted by WKFA with such restrictions is a proper subclass of the languages accepted by arbitrary WKFA in general. In addition, we initiate the study of the language classes characterized by WKFAs with bounded delays. We prove some of the results by means of various relationships between WKFA and sticker systems.


2018 ◽  
Vol 29 (02) ◽  
pp. 251-270 ◽  
Author(s):  
Markus Holzer ◽  
Sebastian Jakobi ◽  
Martin Kutrib

We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on the absence of a forbidden pattern in the (minimal) deterministic state graph. Again with a forbidden pattern approach, we also show that the minimality of REV-DFAs among all equivalent REV-DFAs can be decided. Both forbidden pattern characterizations give rise to [Formula: see text]-complete decision algorithms. In fact, our techniques allow us to construct the minimal REV-DFA for a given minimal DFA. These considerations lead to asymptotic upper and lower bounds on the conversion from DFAs to REV-DFAs. Thus, almost all problems that concern uniqueness and the size of minimal REV-DFAs are solved.


2021 ◽  
Vol 22 (1) ◽  
pp. 7-15
Author(s):  
Alexey E. Zhukov

Recently the reversible cellular automata are increasingly used to build high-performance cryptographic algorithms. The paper establishes a connection between the reversibility of homogeneous one-dimensional binary cellular automata of a finite size and the properties of a structure called binary filter with input memory and such finite automata properties as the prohibitions in automata output and loss of information. We show that finding the preimage for an arbitrary configuration of a one-dimensional cellular automaton of length L with a local transition function f is associated with reversibility of a binary filter with input memory. As a fact, the nonlinear filter with an input memory corresponding to our cellular automaton does not depend on the number of memory cells of the cellular automaton. The results obtained make it possible to reduce the complexity of solving massive enumeration problems related to the issues of reversibility of cellular automata. All the results obtained can be transferred to cellular automata with non-binary cell filling and to cellular automata of dimension greater than 1.


1988 ◽  
Vol 104 (3) ◽  
pp. 363-372 ◽  
Author(s):  
Nicholas C. Barrett ◽  
Denis J. Glencross

2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.


2017 ◽  
Vol 5 (1) ◽  
pp. 8-15
Author(s):  
Sergii Hilgurt ◽  

The multi-pattern matching is a fundamental technique found in applications like a network intrusion detection system, anti-virus, anti-worms and other signature- based information security tools. Due to rising traffic rates, increasing number and sophistication of attacks and the collapse of Moore’s law, traditional software solutions can no longer keep up. Therefore, hardware approaches are frequently being used by developers to accelerate pattern matching. Reconfigurable FPGA-based devices, providing the flexibility of software and the near-ASIC performance, have become increasingly popular for this purpose. Hence, increasing the efficiency of reconfigurable information security tools is a scientific issue now. Many different approaches to constructing hardware matching circuits on FPGAs are known. The most widely used of them are based on discrete comparators, hash-functions and finite automata. Each approach possesses its own pros and cons. None of them still became the leading one. In this paper, a method to combine several different approaches to enforce their advantages has been developed. An analytical technique to quickly advance estimate the resource costs of each matching scheme without need to compile FPGA project has been proposed. It allows to apply optimization procedures to near-optimally split the set of pattern between different approaches in acceptable time.


2009 ◽  
Vol 18 (1) ◽  
pp. 145-158
Author(s):  
Jiang Zhang ◽  
Keyword(s):  

1987 ◽  
Vol 10 (4) ◽  
pp. 415-435
Author(s):  
Kazimierz Wiśniewski
Keyword(s):  

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