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Reasoning about information from multiple parts of a passage to derive an answer is an open challenge for reading-comprehension models. In this paper, we present an approach that reasons about complex questions by decomposing them to…
In essence, the two tagging methods (direct tagging and tagging with sentences compression) are to tag the information we need by using regular expression which basing on the inherent language patterns of the natural language. Though it has…
Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…
We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to…
We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word $w$ into another word, called the reduced word of $w$, that will be at least twice…
Query term matching with document term matching is the basic function of any best effort Information Retrieval models like Vector Space Model. In our problem of SMS based Information Systems we expect common people to participate in…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
Dependency pairs constitute a series of very effective techniques for the termination analysis of term rewriting systems. In this paper, we adapt the static dependency pair framework to logically constrained simply-typed term rewriting…
In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
We discuss a path toward the generalisation of the nested soft-collinear subtraction scheme to arbitrary $2\rightarrow n$ processes. The scheme is designed to provide an efficient and process-independent procedure to extract and regulate…
Multi-step reasoning tasks like mathematical problem solving are vulnerable to cascading failures, where a single incorrect step leads to complete solution breakdown. Current LLM routing methods assign entire queries to one model, treating…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
We developed an algorithm that easily goes from one odd number to the next odd number in binary representation for the reduced forward Collatz map (Syracuse function). The algorithm indicates when an odd number can grow or shrink to the…
Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of…
Through reinforcement learning (RL) with outcome correctness rewards, large reasoning models (LRMs) with scaled inference computation have demonstrated substantial success on complex reasoning tasks. However, the one-sided reward, focused…
Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…
Domain-independent planning is a hard combinatorial problem. Taking into account plan quality makes the task even more difficult. This article introduces Planning by Rewriting (PbR), a new paradigm for efficient high-quality…
Regular expressions are pervasive in modern systems. Many real-world regular expressions are inefficient, sometimes to the extent that they are vulnerable to complexity-based attacks, and while much research has focused on detecting…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…