Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD) and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Then, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Finally, we show how some of the results in the paper can be derived using the I-measure theory, which relates between information theoretic measures and set theory. Our results recover, and sometimes extend, previously known results about the implication problem: the implication of MVDs and FDs can be checked by considering only 2-tuple relations.

IDENTIFIKASI MISKONSEPSI DALAM MENYELESAIKAN SOAL PERTIDAKSAMAAN LINEAR SATU VARIABEL YANG MEMUAT NILAI MUTLAK

This research aims to describe the forms of student misconceptions and the factors that cause misconceptions experienced by students in solving linear inequality problems with one variable containing absolute values in class X SMA Muhammadiyah 1 Pontianak. The subjects of this research were students of class X IPA 3 SMA Muhammadiyah 1 Pontianak, totaling 25 students. The research uses descriptive method as the research method. Case study is a form of research used. The results of the research revealed that the research subjects experienced five forms of misconception, namely notation misconceptions experienced by 1 student or by 4%, generalizing misconceptions experienced by 3 students or by 12%, misconceptions of the application of rules experienced by 6 students or by 24%, calculation misconceptions experienced by 2 students or by 8%, and specialization misconceptions experienced by 3 students or 12%. The misconceptions experienced by these students are caused by wrong intuition and incomplete reasoning, where students' intuitive thoughts that arise spontaneously when solving problems are still wrong and students' reasoning or logic is still wrong in drawing conclusions and being too broad in generalizing. Keywords: Misconceptions, Two-Tier Diagnostic Test, One Variable Linear Inequality Problem with Absolute Values

Fault Attacks on CCA-secure Lattice KEMs

NIST’s post-quantum standardization effort very recently entered its final round. This makes studying the implementation-security aspect of the remaining candidates an increasingly important task, as such analyses can aid in the final selection process and enable appropriately secure wider deployment after standardization. However, lattice-based key-encapsulation mechanisms (KEMs), which are prominently represented among the finalists, have thus far received little attention when it comes to fault attacks.Interestingly, many of these KEMs exhibit structural similarities. They can be seen as variants of the encryption scheme of Lyubashevsky, Peikert, and Rosen, and employ the Fujisaki-Okamoto transform (FO) to achieve CCA2 security. The latter involves re-encrypting a decrypted plaintext and testing the ciphertexts for equivalence. This corresponds to the classic countermeasure of computing the inverse operation and hence prevents many fault attacks.In this work, we show that despite this inherent protection, practical fault attacks are still possible. We present an attack that requires a single instruction-skipping fault in the decoding process, which is run as part of the decapsulation. After observing if this fault actually changed the outcome (effective fault) or if the correct result is still returned (ineffective fault), we can set up a linear inequality involving the key coefficients. After gathering enough of these inequalities by faulting many decapsulations, we can solve for the key using a bespoke statistical solving approach. As our attack only requires distinguishing effective from ineffective faults, various detection-based countermeasures, including many forms of double execution, can be bypassed.We apply this attack to Kyber and NewHope, both of which belong to the aforementioned class of schemes. Using fault simulations, we show that, e.g., 6,500 faulty decapsulations are required for full key recovery on Kyber512. To demonstrate practicality, we use clock glitches to attack Kyber running on a Cortex M4. As we argue that other schemes of this class, such as Saber, might also be susceptible, the presented attack clearly shows that one cannot rely on the FO transform’s fault deterrence and that proper countermeasures are still needed.

UNDERSTANDING OF ONE VARIABLE LINEAR INQUIRY TOPIC SMP STUDENTS WITH SPUR APPROACH

Students' understanding can be known based on 4 components, (1) mastery of procedures (skills), (2) the ability to use properties and principles, (3) the ability to use in the context of the problem (uses), and (4) the ability to make representations ( representation). This qualitative research aims to describe students' understanding of the topic of the linear inequality of one variable guided by the 4 components of understanding. The research subjects were 3 students of grade VIII, with details of 1 student indicated to have fulfilled the 4 components of understanding, 1 student indicated to have fulfilled the 3 components of understanding, and 1 student indicated to have fulfilled the 2 components of understanding. Data collection techniques, namely task-based interviews. The results showed that the skill component of each subject mastered the inequality solving procedure, but there were differences in how to simplify, and the accuracy of each subject was also different. In the properties component, each subject provides truth arguments and conclusions in solving problems, but there are differences when identifying problems by using properties related to inequalities. In the use component, each subject is able to solve contextual problems related to inequalities, but there are differences in how to make the mathematical model. In the representation component, each subject has the ability to solve the inequality, but there are differences in representing the results. Keywords: Understanding, one variable linear inequality, and SPUR

Applied Of Geofencing In Microcontroller With Linear Inequality Approach Of Two Variables

Geofencing merupakan suatu batas virtual yang mengelilingi sebuah area geografis. Area geografis terdiri-dari banyak titik yang mana nilai titik dapat diketahui dengan menggunakan perangkat GPS (Global Potisioning System). Sekarang ini perangkat GPS sudah ada yang berbentuk hanya modul GPS saja, sehingga bisa dikembangkan secara mandiri sesuai kebutuhan. Contoh dari modul tersebut adalah modul GPS GY-NEO6MV2 (Ublox NEO6MV2). Modul ini dapat berkomunikasi dengan mikrokontroler melalui komunikasi serial. Untuk itu penerapan geofencing ke mikrokontroler dapat dilakukan. Wilayah geofencing-nya berbentuk segitiga sembarang yang lokasinya di sekitar kampus Politeknik Negeri Medan, dimana pendekatan Pertidaksamaan Linear Dua Variabel digunakan dalam menentukan wilayah tersebut. Metode penelitian yang digunakan adalah research and development (R&D). Total rata-rata penyimpangan titik ukur jika dibandingkan dengan GPS buatan pabrik adalah 6,455127033 meter. Dan sistem memberikan indikator OUT jika berada di luar wilayah geofencing dan indikator IN jika berada di dalam wilayah geofencing.