Piotr Sapiecha - Academia.edu (original) (raw)

Papers by Piotr Sapiecha

Cornell University - arXiv, Sep 2, 2022

To help prevent hardware security vulnerabilities from propagating to later design stages where f... more To help prevent hardware security vulnerabilities from propagating to later design stages where fixes are costly, it is crucial to identify security concerns as early as possible, such as in RTL designs. In this work, we investigate the practical implications and feasibility of producing a set of security-specific scanners that operate on Verilog source files. The scanners indicate parts of code that might contain one of a set of MITRE's common weakness enumerations (CWEs). We explore the CWE database to characterize the scope and attributes of the CWEs and identify those that are amenable to static analysis. We prototype scanners and evaluate them on 11 open source designs-4 system-on-chips (SoC) and 7 processor cores-and explore the nature of identified weaknesses. Our analysis reported 53 potential weaknesses in the OpenPiton SoC used in Hack@DAC-21, 11 of which we confirmed as security concerns.

Studia Bezpieczeństwa Narodowego, 2014

Neural Networks and Soft Computing, 2003

The article presents methods of dealing with huge data in the domain of neural networks. The deco... more The article presents methods of dealing with huge data in the domain of neural networks. The decomposition of neural networks is introduced and its efficiency is proved by the authors’ experiments. The examinations of the effectiveness of argument reduction in the above filed, are presented. Authors indicate, that decomposition is capable of reducing the size and the complexity of the learned data, and thus it makes the learning process faster or, while dealing with large data, possible. According to the authors’ experiments, in some cases, argument reduction, makes the learning process harder.

We propose the proxy threshold signature scheme with the application of elegant construction of v... more We propose the proxy threshold signature scheme with the application of elegant construction of verifiable delegating key in the ID-based infrastructure, and also with the bilinear pairings. The protocol satisfies the classical security requirements used in the proxy delegation of signing rights. The description of the system architecture and the possible application of the protocol in edge computing designs is enclosed. Keywords—ID-based, proxy, threshold, signature, scheme

Streszczenie. Problem spełnialności formuł rachunku zdań SAT jest jednym z fundamentalnych oraz o... more Streszczenie. Problem spełnialności formuł rachunku zdań SAT jest jednym z fundamentalnych oraz otwartych zadań we współczesnej informatyce. Jest on problemem N P-zupełnym. To znaczy, że wszystkie problemy z klasy N P możemy sprowadzić do problemu SAT w czasie wielomianowym. Co ciekawe, wśród problemów z klasy N P istnieje wiele takich, które są ściśle związanych z kryptologią, na przykład: faktoryzacja liczb-ważna dla RSA, łamanie kluczy szyfrów symetrycznych, znajdowanie kolizji funkcji skrótu i wiele innych. Odkrycie wielomianowego algorytmu dla SAT skutkowałoby rozwiązaniem problemu milenijnego: P vs. N P. Cel ten wydaje się bardzo trudny do osiągnięcia-nie wiadomo nawet czy jest możliwy. Mając nieco mniejsze aspiracje możemy projektować algorytmy heurystyczne lub losowe dla SAT. W związku z tym, głównym celem autorów pracy jest przedstawienie projektu równoległego SAT Solvera bazującego na algorytmie WalkSAT, w tym procesu jego implementacji z wykorzystaniem środowiska programistycznego OpenCL oraz komputera wyposażonego w karty graficzne NVIDIA Tesla. Wraz z dynamicznym rozwojem technologii procesorów typu GPU oraz układów FPGA, jak również przenośnością rozwiązań stworzonych w OpenCL, kierunek takich prac staje się interesujący ze względu na uzyskiwaną efektywność obliczeniową, jak również szybkość prototypowania rozwiązań.

2020 World Conference on Computing and Communication Technologies (WCCCT), 2020

The network operators are facing significant challenges meeting the demand for reliable and effic... more The network operators are facing significant challenges meeting the demand for reliable and efficient operation of network infrastructure, while keeping it secure. Network Functions Virtualization (NFV) and Software-Defined Networking (SDN) technology are emerging as key trends of network architectures, providing flexibility, fast instantiation times, support of Commercial-Off-The-Shelf (COTS) hardware and significant cost savings. On the other hand, the cybersecurity within telecommunication networks has been developed exponentially in the last decade - as more threats appear, technology evolves and business requirements change. One of the most promising trends in cyber defense are Moving Target Defense (MTD) techniques. It's an approach that confuses cyber attackers by making the attack surface dynamic, and thus harder to probe and infiltrate. It's a new technique that represents a significant shift in cyber defense, which has primarily focused on the passive defense of static networks only. The paper describes the concept of the application of combined NFV and SDN technologies to provide a unique platform for implementing MTD techniques for securing the network infrastructure by morphing the logical view of the network topology.

The article is devoted to generation techniques of the new public key crypto-systems, which are b... more The article is devoted to generation techniques of the new public key crypto-systems, which are based on application of indistinguishability obfuscation methods to selected private key crypto-systems. The techniques are applied to symmetric key crypto-system and the target system is asymmetric one. As an input for our approach an implementation of symmetric block cipher with a given private-key is considered. Different obfuscation methods are subjected to processing. The target system would be treated as a public-key for newly created public crypto-system. The approach seems to be interesting from theoretical point of view. Moreover, it can be useful for information protection in a cloud-computing model.

IEEE Wireless Communications, 2020

The development of 5G presents regulators with several security-related challenges. Implementatio... more The development of 5G presents regulators with several security-related challenges. Implementation of a security framework that would be capable of addressing all concerns of users and, by extension, of governments, is one of them. In March 2019, the European Commission presented a plan to achieve, throughout the European Union, a concerted response to security concerns related to 5G networks. This article presents one of the national responses that consists of assessing the risk pursuant to the EN-ISO/IEC 27005 standard and introducing relevant risk mitigation measures. The article focuses on the introduction of a methodical approach to developing 5G security regulations based on an analysis of different risk scenarios. It also strives to propose the applicable government-level mitigation measures aiming to counteract any 5G security threats should these be encountered. When implemented efficiently, the said mitigation measures guarantee that the new networks will be designed in a proper manner. They will also impact cybersecurity of all networks over the coming years.

Computer Science and Mathematical Modelling, 2018

Cloud services are gaining interest and are very interesting option for public administration. Al... more Cloud services are gaining interest and are very interesting option for public administration. Although, there is a lot of concern about security and privacy of storing personal data in cloud. In this work mathematical tools for securing data and hiding computations are presented. Data privacy is obtained by using homomorphic encryption schemes. Computation hiding is done by algorithm cryptographic obfuscation. Both primitives are presented and their application for public administration is discussed.

IFAC Proceedings Volumes, 2004

One of the main objectives for pattern matching methods study is their serious role in the real-w... more One of the main objectives for pattern matching methods study is their serious role in the real-world applications, for example in a branch of Network Intrusion Detection Systems. A NIDS purpose is to protect a local area computer network from unauthorised access. This paper considers a new implementation of the classical Aho-Corasick pattern matching algorithm in hardware. Presented results show that the Aho-Corasick algorithm gives efficient utilization of resources (memory and logic cells) at the cost of lower throughput.

IFAC Proceedings Volumes, 2006

Int rusion Prevention Systems (ll 'Ss) have become widely recognized as a powerful tool a nd an i... more Int rusion Prevention Systems (ll 'Ss) have become widely recognized as a powerful tool a nd an importa nt element of IT sec urity safeguards. Essential to every net work IPS is the a bility to search thro ugh packets a nd identify patteflls that match known attacks. Effi cient string ma tching a lgori thms are therefore im portant fo r id ent if~' i ng these packets at line ra te. In previous art icles a lgorithms like Aho-Corasick, Karp-i{a bin, Bloom filters a nd their hardware implementation architect ures were present ed. The result of the current work is a fixed dicti onary data compression mod ule that. preprocesses input stream for lower resource usage of t.he ma in strin g matching module. The prepa red module matches the extended set of Snort TPS signa t.ures achieving throughput of over 1.7 Ghps on the A It.era St.ratix II device. T he com pression preprocessing module reduces t.he size of pattern dat.ahase hy 40 ' 1" and diminishes t.he module memory resource usage hy ,m %. The proposed compression scheme can be used with every patt ern ma tching algorithm , both in t he softwa re a nd ha rd ware im plementation .

IFAC Proceedings Volumes, 2006

A Bloom filter is a data structure for representing a set of strings in order to support. members... more A Bloom filter is a data structure for representing a set of strings in order to support. membership querie.s. It was first. int.roduced in 1970 for the database query matchmg. Recently this structure ha.s been rediscovered and widely lIsro in the area of network processing. The main prohlems t.hat can he solvro lIsing t.he nloom filt.ers an~: dat.agram t.racehack, mult.i pat.tern mat.ching, packet classification and malicious code fingerprint.ing. In the art.icle we will descrihe our experiences with the implementation of Bloom filters in field-Programmable Gate Arrays for tracing network attacks. The prepared module can operate with the throughput over 1 Gbps and can store up to ::; seconds of traffic using less than 262,144 kB of memory.

2016 2nd International Conference on Frontiers of Signal Processing (ICFSP), 2016

Over the last few years many techniques have been applied to find and mitigate vulnerabilities, m... more Over the last few years many techniques have been applied to find and mitigate vulnerabilities, misuses, cyberattacks and other cyber-security flaws. One of the approaches, which we consider in this paper, is a model-based technique applied to network communication protocols. This idea is not brand new, and model-based techniques have been successfully used to verify and validate the standard models of communication protocols. However, the implementation of network protocols varies from one system to another, and in many cases they miss standards or recommendations. Attackers know these flaws very often and try to use them before everybody else finds them, what can be called "zero-day exploit of communication protocol." To address this issue, a combination of the best features of model-based and anomaly detection techniques could be applied. Treating discovered anomalies as a signature of a cyber-attack or any other malicious activity and focusing on the investigation of them could significantly increase the success rate of the defense against them. In this paper we considered some significant inputs from the research community to model-based anomaly detection in network communication protocols. Then we prepared a synthetic brief of the theories and methods for modelling network protocols as state-machines. Next we examined the application of it in a cyber-security area. Finally we proposed some key directions that actual research should follow to bring some breakthrough results as soon as possible.

Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, 2016

In this article we analyze the problem of optimal location of transportation hubs in Warsaw, name... more In this article we analyze the problem of optimal location of transportation hubs in Warsaw, namely the Park and Ride location problem (P&RP). We take into account the expected travel time using public transport between particular points of the trip. In the currently existing P&R system we have 14 hub locations, and in this case the maximum travel time exceeds 50 minutes. The P&R problem can be reduced to the centers location problem (in our particular approach-the dominating set problem, DS), which is an NP hard problem. In order to determine the optimal locations for P&R two methods: the greedy and the tabu search algorithms were chosen and implemented. According to the computational experiments for the travel time restriction to 50 minutes, we obtain the DS composed of 3 hubs, in contrast to the existing 14 elements. The analysis of the P&R location in time domain is presented in this article in the context of further development of the Warsaw public transportation network, which seems to be interesting.

Advances in Intelligent Systems and Computing, 2016

Nowadays programmable logic structures are commonly used in cryptology. FPGA implementations of c... more Nowadays programmable logic structures are commonly used in cryptology. FPGA implementations of cryptographic and cryptanalytic algorithms combine advantages of an ASIC and a software, offering both great data processing speed and flexibility. In this paper, we present the design and implementation of a system for rapid rainbow tables’ generation. Rainbow tables are commonly used for cryptanalysis of hash functions. The presented approach shows that proposed method may compete with CPU-based approaches when performance is considered, as well as computational complexity, while maintaining low level of programmable structures’ logic element utilization.

Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, 2015

In this paper we consider a hub location problem in a real multimodal public transportation netwo... more In this paper we consider a hub location problem in a real multimodal public transportation network. This problem is also known as the park-and-ride problem. Hubs stations are special facilities that serve as switches in such a network. In practice the set of hubs has a strategic importance, because all of the traffic that passes through the network can be controlled by these elements. From the theoretical point of view, the minimal hub problem is NP hard. Two different approaches to this problem are presented. The first group of methods bases on the greedy algorithms. In the second group the evolutionary strategy is used. The computational results for these algorithms proved a significant efficiency, what can be clearly expressed in terms of an input data reduction and also in quality measure values for the obtained solutions of this problem.

Lecture Notes in Computer Science, 2001

This paper shows that the problem of decomposing a finite function f(A,B) into the form h(g(A),B)... more This paper shows that the problem of decomposing a finite function f(A,B) into the form h(g(A),B), where g is a Boolean function, can be resolved in polynomial time, with respect to the size of the problem. It is also shown that omission of the characteristic of the g function can significantly complicate the problem. Such a general problem belongs to

Cornell University - arXiv, Sep 2, 2022

To help prevent hardware security vulnerabilities from propagating to later design stages where f... more To help prevent hardware security vulnerabilities from propagating to later design stages where fixes are costly, it is crucial to identify security concerns as early as possible, such as in RTL designs. In this work, we investigate the practical implications and feasibility of producing a set of security-specific scanners that operate on Verilog source files. The scanners indicate parts of code that might contain one of a set of MITRE's common weakness enumerations (CWEs). We explore the CWE database to characterize the scope and attributes of the CWEs and identify those that are amenable to static analysis. We prototype scanners and evaluate them on 11 open source designs-4 system-on-chips (SoC) and 7 processor cores-and explore the nature of identified weaknesses. Our analysis reported 53 potential weaknesses in the OpenPiton SoC used in Hack@DAC-21, 11 of which we confirmed as security concerns.

Studia Bezpieczeństwa Narodowego, 2014

Neural Networks and Soft Computing, 2003

The article presents methods of dealing with huge data in the domain of neural networks. The deco... more The article presents methods of dealing with huge data in the domain of neural networks. The decomposition of neural networks is introduced and its efficiency is proved by the authors’ experiments. The examinations of the effectiveness of argument reduction in the above filed, are presented. Authors indicate, that decomposition is capable of reducing the size and the complexity of the learned data, and thus it makes the learning process faster or, while dealing with large data, possible. According to the authors’ experiments, in some cases, argument reduction, makes the learning process harder.

We propose the proxy threshold signature scheme with the application of elegant construction of v... more We propose the proxy threshold signature scheme with the application of elegant construction of verifiable delegating key in the ID-based infrastructure, and also with the bilinear pairings. The protocol satisfies the classical security requirements used in the proxy delegation of signing rights. The description of the system architecture and the possible application of the protocol in edge computing designs is enclosed. Keywords—ID-based, proxy, threshold, signature, scheme

Streszczenie. Problem spełnialności formuł rachunku zdań SAT jest jednym z fundamentalnych oraz o... more Streszczenie. Problem spełnialności formuł rachunku zdań SAT jest jednym z fundamentalnych oraz otwartych zadań we współczesnej informatyce. Jest on problemem N P-zupełnym. To znaczy, że wszystkie problemy z klasy N P możemy sprowadzić do problemu SAT w czasie wielomianowym. Co ciekawe, wśród problemów z klasy N P istnieje wiele takich, które są ściśle związanych z kryptologią, na przykład: faktoryzacja liczb-ważna dla RSA, łamanie kluczy szyfrów symetrycznych, znajdowanie kolizji funkcji skrótu i wiele innych. Odkrycie wielomianowego algorytmu dla SAT skutkowałoby rozwiązaniem problemu milenijnego: P vs. N P. Cel ten wydaje się bardzo trudny do osiągnięcia-nie wiadomo nawet czy jest możliwy. Mając nieco mniejsze aspiracje możemy projektować algorytmy heurystyczne lub losowe dla SAT. W związku z tym, głównym celem autorów pracy jest przedstawienie projektu równoległego SAT Solvera bazującego na algorytmie WalkSAT, w tym procesu jego implementacji z wykorzystaniem środowiska programistycznego OpenCL oraz komputera wyposażonego w karty graficzne NVIDIA Tesla. Wraz z dynamicznym rozwojem technologii procesorów typu GPU oraz układów FPGA, jak również przenośnością rozwiązań stworzonych w OpenCL, kierunek takich prac staje się interesujący ze względu na uzyskiwaną efektywność obliczeniową, jak również szybkość prototypowania rozwiązań.

2020 World Conference on Computing and Communication Technologies (WCCCT), 2020

The network operators are facing significant challenges meeting the demand for reliable and effic... more The network operators are facing significant challenges meeting the demand for reliable and efficient operation of network infrastructure, while keeping it secure. Network Functions Virtualization (NFV) and Software-Defined Networking (SDN) technology are emerging as key trends of network architectures, providing flexibility, fast instantiation times, support of Commercial-Off-The-Shelf (COTS) hardware and significant cost savings. On the other hand, the cybersecurity within telecommunication networks has been developed exponentially in the last decade - as more threats appear, technology evolves and business requirements change. One of the most promising trends in cyber defense are Moving Target Defense (MTD) techniques. It's an approach that confuses cyber attackers by making the attack surface dynamic, and thus harder to probe and infiltrate. It's a new technique that represents a significant shift in cyber defense, which has primarily focused on the passive defense of static networks only. The paper describes the concept of the application of combined NFV and SDN technologies to provide a unique platform for implementing MTD techniques for securing the network infrastructure by morphing the logical view of the network topology.

The article is devoted to generation techniques of the new public key crypto-systems, which are b... more The article is devoted to generation techniques of the new public key crypto-systems, which are based on application of indistinguishability obfuscation methods to selected private key crypto-systems. The techniques are applied to symmetric key crypto-system and the target system is asymmetric one. As an input for our approach an implementation of symmetric block cipher with a given private-key is considered. Different obfuscation methods are subjected to processing. The target system would be treated as a public-key for newly created public crypto-system. The approach seems to be interesting from theoretical point of view. Moreover, it can be useful for information protection in a cloud-computing model.

IEEE Wireless Communications, 2020

The development of 5G presents regulators with several security-related challenges. Implementatio... more The development of 5G presents regulators with several security-related challenges. Implementation of a security framework that would be capable of addressing all concerns of users and, by extension, of governments, is one of them. In March 2019, the European Commission presented a plan to achieve, throughout the European Union, a concerted response to security concerns related to 5G networks. This article presents one of the national responses that consists of assessing the risk pursuant to the EN-ISO/IEC 27005 standard and introducing relevant risk mitigation measures. The article focuses on the introduction of a methodical approach to developing 5G security regulations based on an analysis of different risk scenarios. It also strives to propose the applicable government-level mitigation measures aiming to counteract any 5G security threats should these be encountered. When implemented efficiently, the said mitigation measures guarantee that the new networks will be designed in a proper manner. They will also impact cybersecurity of all networks over the coming years.

Computer Science and Mathematical Modelling, 2018

Cloud services are gaining interest and are very interesting option for public administration. Al... more Cloud services are gaining interest and are very interesting option for public administration. Although, there is a lot of concern about security and privacy of storing personal data in cloud. In this work mathematical tools for securing data and hiding computations are presented. Data privacy is obtained by using homomorphic encryption schemes. Computation hiding is done by algorithm cryptographic obfuscation. Both primitives are presented and their application for public administration is discussed.

IFAC Proceedings Volumes, 2004

One of the main objectives for pattern matching methods study is their serious role in the real-w... more One of the main objectives for pattern matching methods study is their serious role in the real-world applications, for example in a branch of Network Intrusion Detection Systems. A NIDS purpose is to protect a local area computer network from unauthorised access. This paper considers a new implementation of the classical Aho-Corasick pattern matching algorithm in hardware. Presented results show that the Aho-Corasick algorithm gives efficient utilization of resources (memory and logic cells) at the cost of lower throughput.

IFAC Proceedings Volumes, 2006

Int rusion Prevention Systems (ll 'Ss) have become widely recognized as a powerful tool a nd an i... more Int rusion Prevention Systems (ll 'Ss) have become widely recognized as a powerful tool a nd an importa nt element of IT sec urity safeguards. Essential to every net work IPS is the a bility to search thro ugh packets a nd identify patteflls that match known attacks. Effi cient string ma tching a lgori thms are therefore im portant fo r id ent if~' i ng these packets at line ra te. In previous art icles a lgorithms like Aho-Corasick, Karp-i{a bin, Bloom filters a nd their hardware implementation architect ures were present ed. The result of the current work is a fixed dicti onary data compression mod ule that. preprocesses input stream for lower resource usage of t.he ma in strin g matching module. The prepa red module matches the extended set of Snort TPS signa t.ures achieving throughput of over 1.7 Ghps on the A It.era St.ratix II device. T he com pression preprocessing module reduces t.he size of pattern dat.ahase hy 40 ' 1" and diminishes t.he module memory resource usage hy ,m %. The proposed compression scheme can be used with every patt ern ma tching algorithm , both in t he softwa re a nd ha rd ware im plementation .

IFAC Proceedings Volumes, 2006

A Bloom filter is a data structure for representing a set of strings in order to support. members... more A Bloom filter is a data structure for representing a set of strings in order to support. membership querie.s. It was first. int.roduced in 1970 for the database query matchmg. Recently this structure ha.s been rediscovered and widely lIsro in the area of network processing. The main prohlems t.hat can he solvro lIsing t.he nloom filt.ers an~: dat.agram t.racehack, mult.i pat.tern mat.ching, packet classification and malicious code fingerprint.ing. In the art.icle we will descrihe our experiences with the implementation of Bloom filters in field-Programmable Gate Arrays for tracing network attacks. The prepared module can operate with the throughput over 1 Gbps and can store up to ::; seconds of traffic using less than 262,144 kB of memory.

2016 2nd International Conference on Frontiers of Signal Processing (ICFSP), 2016

Over the last few years many techniques have been applied to find and mitigate vulnerabilities, m... more Over the last few years many techniques have been applied to find and mitigate vulnerabilities, misuses, cyberattacks and other cyber-security flaws. One of the approaches, which we consider in this paper, is a model-based technique applied to network communication protocols. This idea is not brand new, and model-based techniques have been successfully used to verify and validate the standard models of communication protocols. However, the implementation of network protocols varies from one system to another, and in many cases they miss standards or recommendations. Attackers know these flaws very often and try to use them before everybody else finds them, what can be called "zero-day exploit of communication protocol." To address this issue, a combination of the best features of model-based and anomaly detection techniques could be applied. Treating discovered anomalies as a signature of a cyber-attack or any other malicious activity and focusing on the investigation of them could significantly increase the success rate of the defense against them. In this paper we considered some significant inputs from the research community to model-based anomaly detection in network communication protocols. Then we prepared a synthetic brief of the theories and methods for modelling network protocols as state-machines. Next we examined the application of it in a cyber-security area. Finally we proposed some key directions that actual research should follow to bring some breakthrough results as soon as possible.

Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, 2016

In this article we analyze the problem of optimal location of transportation hubs in Warsaw, name... more In this article we analyze the problem of optimal location of transportation hubs in Warsaw, namely the Park and Ride location problem (P&RP). We take into account the expected travel time using public transport between particular points of the trip. In the currently existing P&R system we have 14 hub locations, and in this case the maximum travel time exceeds 50 minutes. The P&R problem can be reduced to the centers location problem (in our particular approach-the dominating set problem, DS), which is an NP hard problem. In order to determine the optimal locations for P&R two methods: the greedy and the tabu search algorithms were chosen and implemented. According to the computational experiments for the travel time restriction to 50 minutes, we obtain the DS composed of 3 hubs, in contrast to the existing 14 elements. The analysis of the P&R location in time domain is presented in this article in the context of further development of the Warsaw public transportation network, which seems to be interesting.

Advances in Intelligent Systems and Computing, 2016

Nowadays programmable logic structures are commonly used in cryptology. FPGA implementations of c... more Nowadays programmable logic structures are commonly used in cryptology. FPGA implementations of cryptographic and cryptanalytic algorithms combine advantages of an ASIC and a software, offering both great data processing speed and flexibility. In this paper, we present the design and implementation of a system for rapid rainbow tables’ generation. Rainbow tables are commonly used for cryptanalysis of hash functions. The presented approach shows that proposed method may compete with CPU-based approaches when performance is considered, as well as computational complexity, while maintaining low level of programmable structures’ logic element utilization.

Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, 2015

In this paper we consider a hub location problem in a real multimodal public transportation netwo... more In this paper we consider a hub location problem in a real multimodal public transportation network. This problem is also known as the park-and-ride problem. Hubs stations are special facilities that serve as switches in such a network. In practice the set of hubs has a strategic importance, because all of the traffic that passes through the network can be controlled by these elements. From the theoretical point of view, the minimal hub problem is NP hard. Two different approaches to this problem are presented. The first group of methods bases on the greedy algorithms. In the second group the evolutionary strategy is used. The computational results for these algorithms proved a significant efficiency, what can be clearly expressed in terms of an input data reduction and also in quality measure values for the obtained solutions of this problem.

Lecture Notes in Computer Science, 2001

This paper shows that the problem of decomposing a finite function f(A,B) into the form h(g(A),B)... more This paper shows that the problem of decomposing a finite function f(A,B) into the form h(g(A),B), where g is a Boolean function, can be resolved in polynomial time, with respect to the size of the problem. It is also shown that omission of the characteristic of the g function can significantly complicate the problem. Such a general problem belongs to