We develop an Answer Set Programming (ASP)-based approach for computing the smallest bidirectional macro schemes (BMSs), a fundamental NP-hard optimization problem in dictionary-based compression. Our approach relies on high-level ASP encodings and delegates both the grounding and solving tasks to an off-the-shelf ASP solver. The proposed encoding is compact and extensible, and leverages advanced ASP techniques to improve scalability, including ASP modulo acyclicity and refined declarative encodings of acyclicity constraints. We further show that our ASP encoding can be naturally extended to compute the smallest straight-line programs (SLPs), another important NP-hard measure of repetitiveness. Furthermore, we establish the competitiveness of our approach by empirically contrasting it with a more dedicated MaxSAT-based approach.

The Boolean connectivity problem asks whether the set of satisfying assignments of a given Boolean formula forms a connected subgraph in the n-dimensional hypercube. This problem is known to be coNP-complete, even when restricted to k-Horn formulas for k ≥ 3, as shown by Makino, Tamaki, and Yamamoto. In this paper, we further investigate the complexity of the Boolean connectivity problem for k-Horn formulas, referred to as Conn k-Horn. We first present an exact exponential-time algorithm for Conn k-Horn without any structural restrictions. Our algorithm builds on the deterministic PPZ algorithm proposed by Paturi, Pudlák, and Zane. It runs in O^*(2^{(1-1/2k)n}) time, achieving an exponential improvement over the previously known algorithm for the Boolean connectivity problem of k-CNF formulas, shown by Makino, Tamaki, and Yamamoto. We then examine both algorithmic and hardness results for Conn 3-Horn under bounded variable occurrences. On the algorithmic side, we propose a polynomial-time algorithm for Conn 3-Horn when each clause contains exactly three literals and each variable appears at most three times. This result generalizes to Conn k-Horn under the same structural constraints, in which each clause contains exactly k literals and each variable appears at most k times. On the hardness side, we prove that Conn 3-Horn remains coNP-complete even when restricted to instances in which each variable appears exactly four times.

The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and the existence of only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a ``pre-assignment'' approach for the vertex cover problem as a typical combinatorial optimization problem and discusses its computational complexity. First, we show that the problem is ΣP2-complete in general, while the problem becomes NP-complete when an input graph is bipartite. We then present an O(2.1996^n)-time algorithm for general graphs and an O(1.9181^n)-time algorithm for bipartite graphs, where n is the number of vertices. The latter is based on an FPT algorithm with O*(3.6791^τ) time for vertex cover number τ. Furthermore, we show that the problem for trees can be solved in O(1.4143^n) time.

This paper investigates the (quasi-)periodicity of a string when the string is edited. A string C is called a cover (as known as a quasi-period) of a string T if each character of T lies within some occurrence of C. By definition, a cover of T must be a border of T; that is, it occurs both as a prefix and as a suffix of T. In this paper, we focus on the changes in the longest border and the shortest cover of a string when the string is edited only once. We propose a data structure of size O(n) that computes the longest border and the shortest cover of the string in O(𝓁 log n) time after an edit operation (either insertion, deletion, or substitution of some string) is applied to the input string T of length n, where 𝓁 is the length of the string being inserted or substituted. The data structure can be constructed in O(n) time given string T.

Grammar-based compression is a loss-less data compression scheme that represents a given string $w$ by a context-free grammar that generates only $w$. While computing the smallest grammar which generates a given string $w$ is NP-hard in general, a number of polynomial-time grammar-based compressors which work well in practice have been proposed. RePair, proposed by Larsson and Moffat in 1999, is a grammar-based compressor which recursively replaces all possible occurrences of a most frequently occurring bigrams in the string. Since there can be multiple choices of the most frequent bigrams to replace, different implementations of RePair can result in different grammars. In this paper, we show that the smallest grammars generating the Fibonacci words $F_k$ can be completely characterized by RePair, where $F_k$ denotes the $k$-th Fibonacci word. Namely, all grammars for $F_k$ generated by any implementation of RePair are the smallest grammars for $F_k$, and no other grammars can be the smallest for $F_k$. To the best of our knowledge, Fibonacci words are the first non-trivial infinite family of strings for which RePair is optimal.

The paper describes the folding method of logic functions to reduce the size of memories for keeping the functions. The folding is based on the relation of fractions of logic functions. We show that the fractions of the full adder function have the bit-wise NOT relation and the bit-wise OR relation, and that the memory size becomes half (8-bit). We propose a new 3--1 LUT with the folding mechanisms whcih can implement a full adder with one LUT. A fast carry propagation line is introduced for a multi-bit addition. The folding and fast carry propagation mechanisms are shown to be useful to implement other multi-bit operations and general 4 input functions without extra hardware resources. The paper shows the reduction of the area consumption when using our LUTs compared to the case using 4--1 LUTs on several benchmark circuits.

In the paper, a real-time 64-mono-syllable recognition LSI is presented. The LSI accepts 11.6 msec speech frame and outputs a 6-bit symbol-code for each frame by the end of the next frame with the pipelining manner. The recognition method is based on the Hidden Markov Model and is speaker-independent. An on-chip learning mechanism has also been designed, but the circuit is off-chip at present implementation because of the restriction of LSI area. The LSI is fabricated by VDEC Rohm with 0.6 um process on a 4.5 mm x 4.5 mm chip.

In the paper, we present a real-time speech recognition chip for monosyllables such as A, B, ..., etc. The chip recognizes up to 64 monosyllables based on the Hidden Markov Model (HMM), which is a well known speaker-independent recognition method. The chip accepts a short-speech frame including 256 16-bit digitized samples corresponding to 11.6 msec period, and outputs the 6-bit symbol code of monosyllables for 16 short-frames (corresponding to 185.6 msec). A learning circuit to update HMM parameters for the recognition chip has also been designed, and the recognition chip includes an interface to the learning circuit. We have fabricated the recognition chip by VDEC Rohm 0.6 um process on a 4.5 mm x 4.5 mm chip. We have also made a layout of the entire circuit including the learning circuit by VDEC Rohm 0.35 um process on a 4.9 mm x 4.9 mm chip.

An efficient parallel adder under left-to-right input arrival is proposed. Making full use of the delay of the input arrival, it produces the sum within a small constant delay after the arrival of the final bits. Its amount of hardware is proportional to the operand length. It can be applied to the quotient conversion in an array divider.