相关论文: On instruction sets for Boolean registers in progr…
One of the key strengths of Large Language Models (LLMs) is their ability to interact with humans by generating appropriate responses to given instructions. This ability, known as instruction-following capability, has established a…
In program algebra, an algebraic theory of single-pass instruction sequences, three congruences on instruction sequences are paid attention to: instruction sequence congruence, structural congruence, and behavioural congruence. Sound and…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
Despite widespread deployment of Large Language Models, systematic evaluation of instruction-following capabilities remains challenging. While comprehensive benchmarks exist, focused assessments that quickly diagnose specific instruction…
Large language models (LLMs) could be valuable personal AI agents across various domains, provided they can precisely follow user instructions. However, recent studies have shown significant limitations in LLMs' instruction-following…
We solve the dynamics of on-line Hebbian learning in large perceptrons exactly, for the regime where the size of the training set scales linearly with the number of inputs. We consider both noiseless and noisy teachers. Our calculation…
In this early technical report on an ongoing project, we present -- to the best of our knowledge -- the first study of completeness thresholds for memory safety proofs. Specifically we consider heap-manipulating programs that iterate over…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small…
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
We develop theory concerning non-uniform complexity in a setting in which the notion of single-pass instruction sequence considered in program algebra is the central notion. We define counterparts of the complexity classes P/poly and…
We study the query complexity on slices of Boolean functions. Among other results we show that there exists a Boolean function for which we need to query all but 7 input bits to compute its value, even if we know beforehand that the number…
Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a…
The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
Despite the fact that large language models (LLMs) show exceptional skill in instruction following tasks, this strength can turn into a vulnerability when the models are required to disregard certain instructions. Instruction-following…
In continual learning, understanding the properties of task sequences and their relationships to model performance is important for developing advanced algorithms with better accuracy. However, efforts in this direction remain…
A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x…