Manuel Blum

Lenore Blum, Manuel Blum

We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From this perspective, we develop a formal machine model for consciousness. The model is inspired by Alan Turing's simple yet powerful model of computation and Bernard Baars' theater model of consciousness. Though extremely simple, the model (1) aligns at a high level with many of the major scientific theories of human and animal consciousness, (2) provides explanations at a high level for many phenomena associated with consciousness, (3) gives insight into how a machine can have subjective consciousness, and (4) is clearly buildable. This combination supports our claim that machine consciousness is not only plausible but inevitable.

Manuel Blum, Lenore Blum

We consider the paradoxical concept of free will from the perspective of Theoretical Computer Science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations.

Haofei Yu, Yining Zhao, Lenore Blum et al.

Despite remarkable advances, today's AI systems remain narrow in scope, falling short of the flexible, adaptive, and multisensory intelligence that characterizes human capabilities. This gap has fueled longstanding debates about whether AI might one day achieve human-like generality or even consciousness, and whether theories of consciousness can inspire new architectures for AI. This paper presents an early blueprint for implementing a general AI system, CTM-AI, combining the Conscious Turing Machine (CTM), a formal machine model of consciousness, with today's foundation models. CTM-AI contains an enormous number of powerful processors ranging from specialized experts (e.g., vision-language models and APIs) to unspecialized general-purpose learners poised to develop their own expertise. Crucially, for whatever problem must be dealt with, information from many processors is selected, integrated, and exchanged appropriately to solve the task. CTM-AI achieves state-of-the-art accuracy on MUStARD (72.28) and UR-FUNNY (72.13), outperforming multimodal and multi-agent frameworks. On tool-using and agentic tasks, CTM-AI achieves 10+ points of improvement on StableToolBench and WebArena-Lite. Overall, CTM-AI offers a principled, testable blueprint for general AI inspired by a model of consciousness.

Lenore Blum, Manuel Blum

We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From this perspective, we develop a formal machine model for consciousness. The model is inspired by Alan Turing's simple yet powerful model of computation and Bernard Baars' theater model of consciousness. Though extremely simple, the model (1) aligns at a high level with many of the major scientific theories of human and animal consciousness, (2) provides explanations at a high level for many phenomena associated with consciousness, (3) gives insight into how a machine can have subjective consciousness, and (4) is clearly buildable. This combination supports our claim that machine consciousness is not only plausible but inevitable.

Lenore Blum, Manuel Blum

We have defined the Conscious Turing Machine (CTM) for the purpose of investigating a Theoretical Computer Science (TCS) approach to consciousness. For this, we have hewn to the TCS demand for simplicity and understandability. The CTM is consequently and intentionally a simple machine. It is not a model of the brain, though its design has greatly benefited - and continues to benefit - from neuroscience and psychology. The CTM is a model of and for consciousness. Although it is developed to understand consciousness, the CTM offers a thoughtful and novel guide to the creation of an Artificial General Intelligence (AGI). For example, the CTM has an enormous number of powerful processors, some with specialized expertise, others unspecialized but poised to develop an expertise. For whatever problem must be dealt with, the CTM has an excellent way to utilize those processors that have the required knowledge, ability, and time to work on the problem, even if it is not aware of which ones these may be.

Lenore Blum, Manuel Blum

The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We examine consciousness from the perspective of theoretical computer science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations. In the spirit of Alan Turing's simple yet powerful definition of a computer, the Turing Machine (TM), and perspective of computational complexity theory, we formalize a modified version of the Global Workspace Theory (GWT) of consciousness originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, Jean-Pierre Changeaux and others. We are not looking for a complex model of the brain nor of cognition, but for a simple computational model of (the admittedly complex concept of) consciousness. We do this by defining the Conscious Turing Machine (CTM), also called a conscious AI, and then we define consciousness and related notions in the CTM. While these are only mathematical (TCS) definitions, we suggest why the CTM has the feeling of consciousness. The TCS perspective provides a simple formal framework to employ tools from computational complexity theory and machine learning to help us understand consciousness and related concepts. Previously we explored high level explanations for the feelings of pain and pleasure in the CTM. Here we consider three examples related to vision (blindsight, inattentional blindness, and change blindness), followed by discussions of dreams, free will, and altered states of consciousness.

Manuel Blum, Lenore Blum

The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. This paper studies consciousness from the perspective of theoretical computer science. It formalizes the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. Our major contribution lies in the precise formal definition of a Conscious Turing Machine (CTM), also called a Conscious AI. We define the CTM in the spirit of Alan Turing's simple yet powerful definition of a computer, the Turing Machine (TM). We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness. After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the breadth of related concepts that the model explains easily and naturally, and the extent of its agreement with scientific evidence.

Elan Rosenfeld, Santosh Vempala, Manuel Blum

Password users frequently employ passwords that are too simple, or they just reuse passwords for multiple websites. A common complaint is that utilizing secure passwords is too difficult. One possible solution to this problem is to use a password schema. Password schemas are deterministic functions which map challenges (typically the website name) to responses (passwords). Previous work has been done on developing and analyzing publishable schemas, but these analyses have been information-theoretic, not complexity-theoretic; they consider an adversary with infinite computing power. We perform an analysis with respect to adversaries having currently achievable computing capabilities, assessing the realistic practical security of such schemas. We prove for several specific schemas that a computer is no worse off than an infinite adversary and that it can successfully extract all information from leaked challenges and their respective responses, known as challenge-response pairs. We also show that any schema that hopes to be secure against adversaries with bounded computation should obscure information in a very specific way, by introducing many possible constraints with each challenge-response pair. These surprising results put the analyses of password schemas on a more solid and practical footing.

Maria Hügle, Simon Heller, Manuel Watter et al.

Implantable, closed-loop devices for automated early detection and stimulation of epileptic seizures are promising treatment options for patients with severe epilepsy that cannot be treated with traditional means. Most approaches for early seizure detection in the literature are, however, not optimized for implementation on ultra-low power microcontrollers required for long-term implantation. In this paper we present a convolutional neural network for the early detection of seizures from intracranial EEG signals, designed specifically for this purpose. In addition, we investigate approximations to comply with hardware limits while preserving accuracy. We compare our approach to three previously proposed convolutional neural networks and a feature-based SVM classifier with respect to detection accuracy, latency and computational needs. Evaluation is based on a comprehensive database with long-term EEG recordings. The proposed method outperforms the other detectors with a median sensitivity of 0.96, false detection rate of 10.1 per hour and median detection delay of 3.7 seconds, while being the only approach suited to be realized on a low power microcontroller due to its parsimonious use of computational and memory resources.

Manuel Blum, Santosh Vempala

What can humans compute in their heads? We are thinking of a variety of Crypto Protocols, games like Sudoku, Crossword Puzzles, Speed Chess, and so on. The intent of this paper is to apply the ideas and methods of theoretical computer science to better understand what humans can compute in their heads. For example, can a person compute a function in their head so that an eavesdropper with a powerful computer --- who sees the responses to random input --- still cannot infer responses to new inputs? To address such questions, we propose a rigorous model of human computation and associated measures of complexity. We apply the model and measures first and foremost to the problem of (1) humanly computable password generation, and then consider related problems of (2) humanly computable "one-way functions" and (3) humanly computable "pseudorandom generators". The theory of Human Computability developed here plays by different rules than standard computability, and this takes some getting used to. For reasons to be made clear, the polynomial versus exponential time divide of modern computability theory is irrelevant to human computation. In human computability, the step-counts for both humans and computers must be more concrete. Specifically, we restrict the adversary to at most 10^24 (Avogadro number of) steps. An alternate view of this work is that it deals with the analysis of algorithms and counting steps for the case that inputs are small as opposed to the usual case of inputs large-in-the-limit.

Jeremiah Blocki, Manuel Blum, Anupam Datta et al.

An interesting challenge for the cryptography community is to design authentication protocols that are so simple that a human can execute them without relying on a fully trusted computer. We propose several candidate authentication protocols for a setting in which the human user can only receive assistance from a semi-trusted computer --- a computer that stores information and performs computations correctly but does not provide confidentiality. Our schemes use a semi-trusted computer to store and display public challenges $C_i\in[n]^k$. The human user memorizes a random secret mapping $σ:[n]\rightarrow\mathbb{Z}_d$ and authenticates by computing responses $f(σ(C_i))$ to a sequence of public challenges where $f:\mathbb{Z}_d^k\rightarrow\mathbb{Z}_d$ is a function that is easy for the human to evaluate. We prove that any statistical adversary needs to sample $m=\tildeΩ(n^{s(f)})$ challenge-response pairs to recover $σ$, for a security parameter $s(f)$ that depends on two key properties of $f$. To obtain our results, we apply the general hypercontractivity theorem to lower bound the statistical dimension of the distribution over challenge-response pairs induced by $f$ and $σ$. Our lower bounds apply to arbitrary functions $f $ (not just to functions that are easy for a human to evaluate), and generalize recent results of Feldman et al. As an application, we propose a family of human computable password functions $f_{k_1,k_2}$ in which the user needs to perform $2k_1+2k_2+1$ primitive operations (e.g., adding two digits or remembering $σ(i)$), and we show that $s(f) = \min\{k_1+1, (k_2+1)/2\}$. For these schemes, we prove that forging passwords is equivalent to recovering the secret mapping. Thus, our human computable password schemes can maintain strong security guarantees even after an adversary has observed the user login to many different accounts.

Jeremiah Blocki, Manuel Blum, Anupam Datta

We introduce GOTCHAs (Generating panOptic Turing Tests to Tell Computers and Humans Apart) as a way of preventing automated offline dictionary attacks against user selected passwords. A GOTCHA is a randomized puzzle generation protocol, which involves interaction between a computer and a human. Informally, a GOTCHA should satisfy two key properties: (1) The puzzles are easy for the human to solve. (2) The puzzles are hard for a computer to solve even if it has the random bits used by the computer to generate the final puzzle --- unlike a CAPTCHA. Our main theorem demonstrates that GOTCHAs can be used to mitigate the threat of offline dictionary attacks against passwords by ensuring that a password cracker must receive constant feedback from a human being while mounting an attack. Finally, we provide a candidate construction of GOTCHAs based on Inkblot images. Our construction relies on the usability assumption that users can recognize the phrases that they originally used to describe each Inkblot image --- a much weaker usability assumption than previous password systems based on Inkblots which required users to recall their phrase exactly. We conduct a user study to evaluate the usability of our GOTCHA construction. We also generate a GOTCHA challenge where we encourage artificial intelligence and security researchers to try to crack several passwords protected with our scheme.

Jeremiah Blocki, Manuel Blum, Anupam Datta

We introduce quantitative usability and security models to guide the design of password management schemes --- systematic strategies to help users create and remember multiple passwords. In the same way that security proofs in cryptography are based on complexity-theoretic assumptions (e.g., hardness of factoring and discrete logarithm), we quantify usability by introducing usability assumptions. In particular, password management relies on assumptions about human memory, e.g., that a user who follows a particular rehearsal schedule will successfully maintain the corresponding memory. These assumptions are informed by research in cognitive science and validated through empirical studies. Given rehearsal requirements and a user's visitation schedule for each account, we use the total number of extra rehearsals that the user would have to do to remember all of his passwords as a measure of the usability of the password scheme. Our usability model leads us to a key observation: password reuse benefits users not only by reducing the number of passwords that the user has to memorize, but more importantly by increasing the natural rehearsal rate for each password. We also present a security model which accounts for the complexity of password management with multiple accounts and associated threats, including online, offline, and plaintext password leak attacks. Observing that current password management schemes are either insecure or unusable, we present Shared Cues--- a new scheme in which the underlying secret is strategically shared across accounts to ensure that most rehearsal requirements are satisfied naturally while simultaneously providing strong security. The construction uses the Chinese Remainder Theorem to achieve these competing goals.