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As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…
We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive…
Rice's Theorem states that every nontrivial language property of the recursively enumerable sets is undecidable. Borchert and Stephan initiated the search for complexity-theoretic analogs of Rice's Theorem. In particular, they proved that…
We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4. Key to our approach is reflection: a Boolean checker function whose soundness is fully proved in Lean and executed as compiled native code.…
The goal of grammar compression is to construct a small sized context free grammar which uniquely generates the input text data. Among grammar compression methods, RePair is known for its good practical compression performance. MR-RePair…
We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been…
Petri nets are a mathematical language for modeling and reasoning about distributed systems. In this paper we propose an approach to Petri nets for embedding reversibility, i.e., the ability of reversing an executed sequence of operations…
They run our lives, if you believe the hype in the news, but there is no precise definition of "algorithms" which is generally accepted by the mathematicians, logicians and computer scientists who create and study them. My main aims here…
Cell-penetrating peptides (CPPs) are powerful vectors for the intracellular delivery of a diverse array of therapeutic molecules. Despite their potential, the rational design of CPPs remains a challenging task that often requires extensive…
Several cryptographic systems depend upon the computational difficulty of reversing cryptographic hash functions. Robust hash functions transform inputs to outputs in such a way that the inputs cannot be later retrieved in a reasonable…
We propose an automated verification technique for hypersafety properties, which express sets of valid interrelations between multiple finite runs of a program. The key observation is that constructing a proof for a small representative set…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
Deep learning has redefined the field of artificial intelligence (AI) thanks to the rise of artificial neural networks, which are architectures inspired by their neurological counterpart in the brain. Through the years, this dualism between…
When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a…
Recurrent neural networks (RNNs) provide state-of-the-art performance in processing sequential data but are memory intensive to train, limiting the flexibility of RNN models which can be trained. Reversible RNNs---RNNs for which the…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Verifying the input-output relationships of a neural network so as to achieve some desired performance specification is a difficult, yet important, problem due to the growing ubiquity of neural nets in many engineering applications. We use…