The Infinity Machine: Demis Hassabis, DeepMind, and the Quest for Superintelligence
by Sebastian Mallaby; · 30 Mar 2026 · 607pp · 161,998 words
were brainstorming these big ideas. There was this thrill of unbridled creation.” In the early 1990s, video games were built on software platforms known as “finite-state machines.” Characters toggled crudely between a limited number of states—a monster might run, attack, or eat, for example. But Molyneux insisted that the
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finite-state architecture should be pushed to the max, so that the digital figures in Theme Park would exhibit a far greater range of behaviors. They would
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followers.[18] Hassabis was drawn to Black & White by the opportunity to experiment with AI programming. Whereas the characters in Theme Park had been complex finite-state machines, obeying fixed rules governing their preferences, Black & White would be the first game in which the avatars’ internal rules changed based on feedback. If
Artificial Intelligence: A Modern Approach
by Stuart Russell and Peter Norvig · 14 Jul 2019 · 2,466pp · 668,761 words
when written in a factored-representation language such as propositional logic and around 1038 pages when written in an atomic language such as that of finite-state automata. On the other hand, reasoning and learning become more complex as the expressive power of the representation increases. To gain the benefits of expressive
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anywhere in the state space; therefore a complete algorithm must be capable of systematically exploring every state that is reachable from the initial state. In finite state spaces that is straightforward to achieve: as long as we keep track of paths and cut off ones that are cycles (e.g. Arad to
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are lavender, and potential future nodes have faint dashed lines. Expanded nodes with no descendants in the frontier (very faint lines) can be discarded. For finite state spaces that are trees it is efficient and complete; for acyclic state spaces it may end up expanding the same state many times via different
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-first and breadth-first search. Like depth-first search, its memory requirements are modest: O(bd) when there is a solution, or O(bm) on finite state spaces with no solution. Like breadth-first search, iterative deepening is optimal for problems where all actions have the same cost, and is complete on
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finite acyclic state spaces, or on any finite state space when we check nodes for cycles all the way up the path. Figure 3.12 Iterative deepening and depth-limited tree-like search. Iterative
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versions which don’t check for repeated states. For graph searches which do check, the main differences are that depth-first search is complete for finite state spaces, and the space and time complexities are bounded by the size of the state space (the number of vertices and edges, |V | + |E|). Figure
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search for Bucharest with the straight-line distance heuristic hSLD. Nodes are labeled with their h-values. Greedy best-first graph search is complete in finite state spaces, but not in infinite ones. The worst-case time and space complexity is O(|V|). With a good heuristic function, however, the complexity can
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the earlier incarnation of the current state, so the new incarnation can be discarded. With this check, we ensure that the algorithm terminates in every finite state space, because every path must reach a goal, a dead end, or a repeated state. Notice that the algorithm does not check whether the current
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by the work of John Koza (1992, 1994), but it goes back at least to early experiments with machine code by Friedberg (1958) and with finite-state automata by Fogel et al. (1966). As with genetic algorithms, there is debate about the effectiveness of the technique. Koza et al. (1999) describe experiments
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that “infinite horizon” does not necessarily mean that all state sequences are infinite; it just means that there is no fixed deadline. There can be finite state sequences in an infinite-horizon MDP that contains a terminal state. The next question we must decide is how to calculate the utility of state
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, so it is a solution to the Bellman equations, and πi must be an optimal policy. Because there are only finitely many policies for a finite state space, and each iteration can be shown to yield a better policy, policy iteration must terminate. The algorithm is shown in Figure 16.9. As
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) state space. This means we will have to redesign the dynamic programming algorithms from Sections 16.2.1 and 16.2.2, which assumed a finite state space and a finite number of actions. Here we describe a value iteration algorithm designed specifically for POMDPs, followed by an online decision-making algorithm
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of POMDP value iteration. Other algorithms soon followed, including an approach due to Hansen (1998) that constructs a policy incrementally in the form of a finite-state automaton whose states define the possible belief states of the agent. More recent work in AI has focused on point-based value iteration methods that
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for games that will be played an infinite number of rounds. For this reason, it is standard to represent strategies for infinitely repeated games as finite state machines (FSMs) with output. Figure 17.3 illustrates a number of FSM strategies for the iterated prisoner’s dilemma. Consider the Tit-for-Tat strategy
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1. Row 3: Column 1, 0.8516. Column 2, 0.9078. Column 3, 0.9578. Column 4, positive 1. Figure 17.3Some common, colorfully named finite-state machine strategies for the infinitely repeated prisoner’s dilemma. The HAWK and DOVE strategies are simpler: HAWK simply plays testify on every round, while DOVE
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to compute the average over the finite repeating sequence. In what follows, we will assume that players in an infinitely repeated game simply choose a finite state machine to play the game on their behalf. We don’t impose any constraints on these machines: they can be as big and elaborate as
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players want. When all players have chosen a finite state machine to play on their behalf, then we can compute the payoffs for each player using the limit of means approach as described above. In
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might have adopted it. We can also get different solutions by changing the agents, rather than changing the rules of engagement. Suppose the agents are finite state machines with n states and they are playing a game with m > n total steps. The agents are thus incapable of representing the number of
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extensively by Axelrod (1985) and Poundstone (1993). Repeated games were introduced by Luce and Raiffa (1957), and Abreu and Rubinstein (1988) discuss the use of finite state machines for repeated games—technically, Moore machines. The text by Mailath and Samuelson (2006) concentrates on repeated games. Games of partial information in extensive form
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particular properties.” Norvig (2009) gives some examples of tasks that can be accomplished with n-gram models. Chomsky (1956, 1957) pointed out the limitations of finite-state models compared with context-free models, concluding, “Probabilistic models give no particular insight into some of the basic problems of syntactic structure.” This is true
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gone too far (Church and Hestness, 2019). Early linguists concentrated on actual language usage data, including frequency counts. Noam Chomsky (1956) demonstrated the limitations of finite-state models, leading to an emphasis on theoretical studies of syntax, disregarding actual language performance. This approach dominated for twenty years, until empiricism made a comeback
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render the resulting path planning problem computationally difficult. Figure 26.32(a) Genghis, a hexapod robot. (Image courtesy of Rodney A. Brooks.) (b) An augmented finite state machine (AFSM) that controls one leg. The AFSM reacts to sensor feedback: if a leg is stuck during the forward swinging phase, it will be
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motion is blocked, simply retract it, lift it higher, and try again. The resulting controller is shown in Figure 26.32(b) as a simple finite state machine; it constitutes a reflex agent with state, where the internal state is represented by the index of the current machine state (s1 through s4
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). 26.9.2Subsumption architectures The subsumption architecture (Brooks, 1986) is a framework for assembling reactive controllers out of finite state machines. Nodes in these machines may contain tests for certain sensor variables, in which case the execution trace of a
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finite state machine is conditioned on the outcome of such a test. Arcs can be tagged with messages that will be generated when traversing them, and that
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are sent to the robot’s motors or to other finite state machines. Additionally, finite state machines possess internal timers (clocks) that control the time it takes to traverse an arc. The resulting machines are called augmented
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finite state machines (AFSMs), where the augmentation refers to the use of clocks. An example of a simple AFSM is the four-state machine we just talked
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). A Bayesian approach to relevance in game playing. AIJ, 97, 195–242. Baum, L. E. and Petrie, T. (1966). Statistical inference for probabilistic functions of finite state Markov chains. Annals of Mathematical Statistics, 41, 1554–1563. Baxter, J. and Bartlett, P. (2000). Reinforcement learning in POMDPs via direct gradient ascent. In ICML
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-linear models. In ACL-04. Clarke, A. C. (1968). 2001: A Space Odyssey. Signet. Clarke, E. and Grumberg, O. (1987). Research on automatic verification of finite-state concurrent systems. Annual Review of Computer Science, 2, 269–290. Clearwater, S. H. (Ed.). (1996). Market-Based Control. World Scientific. Clocksin, W. F. and Mellish
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, 23–41. Robinson, S. (2002). Computer scientists find unexpected depths in airfare search problem. SIAM News, 35(6). Roche, E. and Schabes, Y. (Eds.). (1997). Finite–State Language Processing. Bradford Books. Rock, I. (1984). Perception. W. H. Freeman. Rokicki, T., Kociemba, H., Davidson, M., and Dethridge, J. (2014). The diameter of the
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, 1100 ADP (adaptive dynamic programming), 844, 869 adversarial example, 821, 838 adversarial search, 192 adversarial training, 975 adversary argument, 154 Advice Taker, 37 AFSM (augmented finite state machine), 976 Agarwal, P. 974, 986, 1041, 1105, 1112 agent, 21, 54, 78 active learning, 848 architecture of, 65, 1069 autonomous, 228 benevolent, 589 components
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second-price, 626 truth-revealing, 625 Vickrey, 626 Audi, R., 1058, 1086 Auer, P., 587, 1086 Auer, S., 334, 357, 1088, 1103 augmentation, 902 augmented finite state machine (AFSM), 976 augmented grammar, 892 Aumann, R., 637, 1086 AURA (theorem prover), 327, 331 Auray, J. R, 549, 1087 Austerweil, J. L., 872, 1099
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.E., 79, 162, 296, 398, 400, 401, 983, 1095 filtering, 150, 353, 484–485, 514, 578, 795, 938 assumed-density, 517 Fine, S., 516, 1095 finite state machine, 604 Fink, D., 137, 161, 1106 Finkelstein, L., 191, 1089 Finn, C., 737, 841, 986, 1095, 1103 Finney, D. I., 473, 1095 Firat, O
Optimization Methods in Finance
by Gerard Cornuejols and Reha Tutuncu · 2 Jan 2006 · 130pp · 11,880 words
the proof of Theorem 3.2 can naturally be used for detection of arbitrage opportunities. However, as we discussed above, this argument works only for finite state spaces. In this section, we discuss how LP formulations can be used to detect arbitrage opportunities without limiting consideration to
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finite state spaces. The price we pay for this flexibility is the restriction on the selection of the securities: we only consider the prices of a set
Syntactic Structures
by Noam Chomsky · 17 Oct 2008
primitives were indepen dently defined, not a product of more basic semantic, functional or notional concepts (chapter 2), that they could not be fonnulated through finite-state Markov processes (chapter 3), and that restricting rule schemas to those of phrase structure grammars yielded clumsiness and missed insights and elegance which would be
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produced i n this way. Any language that can be produced by a machine of this sort we call a finite state language ; and we can call the machine itself a finite state grammar. A finite state grammar can be represented graphically i n the form o f a "state diagram".l For example, the grammar
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, and we can have any n umber of closed loops of any length. The machines that produce languages in this manner are known mathematically as "finite state Markov processes. " To complete this elementary communication theoretic model for language, we assign a probability to each transition from state to state. We can then
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this point of view in the syntactic study of some language such as English or a formalized system of mathematics. Any attempt to construct a finite state grammar for E nglish runs into serious difficulties and complications at the very outset, as the reader can easily convince himself. However, i t is
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, 1955), 02. 21 AN ELEMENTARY LINGUISTIC THEORY example, i n v iew o f the foIIowingmore general remark about English : (9) English is not a finite state language. That is, it is impossible, not just difficult, to construct a device of the type described above (a diagram such as (7) or (8
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fol l owed by the identical string X, and only these. . . . We can easily show that each of these three la nguages is not a finite state language. Similarly, languages such as ( 1 0) where the a's and b's i n question are not consecutive, but are embedded i n
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exhausting these possibili ties) will have all of the mirror image properties of ( I O ii) which exclude ( I O ii) from the set of finite state languages. Thus we can find various kinds of non3 See my "Three models for the descri;:>tion of language," I. R.E. Transaclions on lnjormalion
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of (9). Notice in particular that the set of well-formed formulas of any formalized system of mathematics or logic will fail to wnstitute a finite state language, because of paired parentheses or equivalent restrictions. AN ELEMENTARY LINGUISTIC THEORY 23 fi nite state models within English. This is a rough indication of
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than a mi llion words. Such arbitrary limitations serve no useful purpose, however. The point i s that there are processes of sentence formation that finite state grammars are i ntrinsically not equipped to handle. If these pro cesses have no finite limit, we can prove the literal inapplicabi l i ty
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of this elementary theory. I f the processes have a limit, then the construction of a finite state grammar will not be litera lly out of the question, since it will be possible to list the sentences, and a list is essent ially
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a trivial finite state grammar. But this grammar will be so complex that it will be of little use or i nterest. In general, the assumption that languages are
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to simplify 24 SYNTACTIC STRUCTURES the description of these languages. If a grammar does not have recursive devices (closed loops, as in (8), in the finite state grammar) it will be prohibitively complex. If it does have recursive devices of some sort, it will produce infinitely many sentences. In short, the approach
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to the analysis of grammaticalness suggest ed here in terms of a finite state M arkov process that produces sentences from left to right, appears to lead to a dead end just as surely as the proposals rejected in
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simple linear method of representation, but to generate at least one such level from left to right by a device with more capacity than a finite state Markov process. There are so many difficulties with the notion of linguistic level based on left to right generation, both in terms of complexity of
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manner i n terms o f a single level (i.e., if it is a finite state language) then this description may i ndeed be simplified by construction of such higher levels ; but to generate non-finite state languages such as English we need fundamentally different methods, and a more general concept of "linguistic
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this approach any further. The grammars that we discuss below that do not generate from left to right also correspond to processes less elementary than finite state Markov processes. But they are perhaps less powerful than the kind of device that would be required for direct left-to-right generation of English
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formal way in terms of the associated diagrams. 4.2 In § 3 we considered languages, calJed "fin i tt: state languages", which were generated by finite state M arkov processes. Now we are considering terminal languages that are generated by systems of the form [L, Fl. These two types of languages are
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related in the fol lowing way Theorem : Every finite state language is a term inal language, but there are terminal languages which are not finite state languages.4 The import of this theorem is that description in terms of phrase structure is essentially more
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powerful than description in terms of the elementary theory presented above in § 3. As examples of terminal languages that are not finite state l anguages we have the languages ( ! o i), ( 1 0 ii) discussed in § 3. Thus the language ( ! o i), consisting of all and only the
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n § 3 we pointed out that the languages ( l O i) and ( l O ii) corre spond to subparts of English, and that therefore the finite state M arkov process model is not adequate for English. We n ow see that the phrase structure model does not fail in such cases. We
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more powerful than description i n terms of phrase structure, j ust as the latter is essentially more powerfull than description i n terms of finite state Markov processes that generate sentences from left to right. In particular, such languages as ( l O iii) which lie beyond the bounds of phrase structure
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the notion of statistical order of approximation). In carrying out this independent and formal study, we find that a simple mode! of language as a finite state M arkov process that produces sentences from left to right is not acceptable, and that such fairly abstract l inguistic levels as phrase structure and
Applied Cryptography: Protocols, Algorithms, and Source Code in C
by Bruce Schneier · 10 Nov 1993
the stuff that went in and the computer’s current state. That means that any random-number generator on a computer (at least, on a finite-state machine) is, by definition, periodic. Anything that is periodic is, by definition, predictable. And if something is predictable, it can’t be random. A true
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that there is honest-to-goodness randomness in the real world. But can we preserve that randomness in the deterministic world of computer chips and finite-state machines? Philosophy aside, from our point of view a sequence generator is real random if it has this additional third property: 3. It cannot be
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field. The first approach treats a cryptographic protocol as any other computer program and attempts to prove correctness. Some researchers represent a protocol as a finite-state machine [1449,1565], others use extensions of first-order predicate calculus [822], and still others use specification languages to analyze protocols [1566]. However, proving correctness
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transform the wave function, altering the entire set of states in a single operation. In this way, a quantum computer is an improvement over classical finite-state automata: It uses quantum properties to allow it to factor in polynomial time, theoretically allowing one to break cryptosystems based on factoring or the discrete
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a keystream generator must generate the same output on both the encryption and decryption ends, it must be deterministic. Because it is implemented in a finite-state machine (i.e., a computer), the sequence will eventually repeat. These keystream generators are called periodic. Except for one-time pads, all keystream generators are
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and space required to solve the hardest instance of a problem on a theoretical computer known as a Turing machine . A Turing machine is a finite-state machine with an infinite read-write memory tape. It turns out that a Turing machine is a realistic model of computation. Problems that can be
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, or linear span. This is defined as the length, n, of the shortest LFSR that can mimic the generator output. Any sequence generated by a finite-state machine over a finite field has a finite linear complexity [1006]. Linear complexity is important because a simple algorithm, called the Berlekamp-Massey algorithm, can
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for the Motorola DSP56000,” Advances in Cryptology—EUROCRYPT ’90 Proceedings, Springer–Verlag, 1991, pp. 230–244. 510. C. Dwork and L. Stockmeyer, “Zero–Knowledge with Finite State Verifiers,” Advances in Cryptology—CRYPTO ’88 Proceedings, Springer–Verlag, 1990, pp. 71–75. 511. D.E. Eastlake, S.D. Crocker, and J.I. Schiller, “Randomness
Masterminds of Programming: Conversations With the Creators of Major Programming Languages
by Federico Biancuzzi and Shane Warden · 21 Mar 2009 · 496pp · 174,084 words
domain. How do you make the idea of syntax-driven transformations accessible to users who might not know very much or anything at all about finite-state machines and push-down automata? Al: Certainly as a user of AWK, you don’t need to know about these concepts. On the other hand
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, if you’re into language design and implementation, knowledge of finite-state machines and context-free grammars is essential. Should a user of lex or yacc understand the context-free grammar even if the programs they produce
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don’t require their users to understand them? Al: Most users of lex can use lex without understanding what a finite-state machine is. A user of yacc is really writing a context-free grammar, so from that perspective, the user of yacc certainly gets to appreciate
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, particularly regular expressions and context-free grammars, for describing the important syntactic features of programming languages. The automata that recognize these formal languages, such as finite-state machines and push-down automata, can serve as models for the algorithms used by compilers to scan and parse programs. Perhaps the greatest benefit of
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is currently an active research area. Many researchers are exploring parallel hardware and software implementations of pattern-matching algorithms like the Aho-Corasick algorithm or finite-state algorithms. Some of the strong motivators are genomic analyses and intrusion detection systems. What motivated you and Corasick to develop the Aho-Corasick algorithm? Al
Turing's Cathedral
by George Dyson · 6 Mar 2012
storage, putting the cost of a cerebral cortex at £300 per annum—his King’s College fellowship for the year. Viewed as part of a finite-state Turing machine, the delay line represented a continuous loop of tape, 1,000 squares in length and making 1,000 complete passes per second under
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microseconds count, they are closer, from the bottom up, in time. Meaning just seems to “come to mind” first. An Internet search engine is a finite-state, deterministic machine, except at those junctures where people, individually and collectively, make a nondeterministic choice as to which results are selected as meaningful and given
Monte Carlo Simulation and Finance
by Don L. McLeish · 1 Apr 2005
R, rbinom(m,n,p) will generate a vector of length m of Binomial(n, p) variates. Random Samples Associated with Markov Chains Consider a finite state Markov Chain, a sequence of (discrete) random variables X1 , X2 , . . .each of which takes integer values 1, 2, . . . N (called states). The number of states
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states of a Markov chain, but we will give some examples of this later. For the present we restrict attention to the case of a finite state space. The transition probability matrix is a matrix P describing the conditional probability of moving between possible states of the chain, so that P [Xn
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run the chain from an arbitrary starting value and then delete the initial transient. An alternative elegant method that is feasible at least for some finite state Markov chains is the method of “coupling from the past” due to Propp and Wilson (1996). We assume that we are able to generate transitions
Types and Programming Languages
by Benjamin C. Pierce · 4 Jan 2002 · 647pp · 43,757 words
unfamiliar with the underlying theories. One well-known instance of this sort of lightweight formal methods is model checkers, tools that search for errors in finite-state systems such as chip designs or communication protocols. Another that is growing in popularity is run-time monitoring, a collection of techniques that allow a
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x if y Î reachable(x). 21.5.11 Definition An invertible generating function F is said to be finite state if reachable(x) is finite for each x Î U. For a finite-state generating function, the search space explored by gfp is finite and gfp always terminates: 21.5.12 Theorem If
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reachableF(X) is finite, then gfpF(X) is defined. Consequently, if F is finite state, then gfpF(X) terminates for any finite X ⊆ U. Proof: For each recursive call gfp(Y) in the call graph generated by the original invocation
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sufficient termination condition for all of them is the same as that of the original gfp algorithm: they terminate on all inputs when F is finite state. [3]A tail-recursive call (or tail call) is a recursive call that is the last action of the calling function-i.e., such that
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generic algorithms for checking membership in a set defined as the greatest fixed point of a generating function F, assuming that F is invertible and finite state; separately, we have shown how to define subtyping between infinite trees as the greatest fixed point of a particular generating function S. The obvious next
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to justify the statement T<:T is infinite. 21.7.4 Proposition The restriction Sr of the generating function S to regular tree types is finite state. Proof: We need to show that for any pair (S, T)of regular tree types, the set is finite. Observe that ; the latter is finite
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characterize the generating functions F for which lfp is guaranteed to terminate on all finite inputs. For this, some new terminology is helpful. Given a finite-state generating function F Î P(U) → P(U), the partial function (or just height) is the least partial function satisfying the following condition:[2] (Note
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check that, if y Î support(x) and both height(x) and height(y) are defined, then height(y) < height(x). Now, if F is finite state and finite height, then lfp(X) terminates for any finite input set X ⊆ U. To see this, observe that, since F is
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finite state, for every recursive call lfp(Y) descended from the original call lfp(X), the set Y is finite. Since F is finite height, h(Y) =
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, 16 families (of terms, types), 462 Featherweight Java, 247–264 fields, see instance variables; records finalizers, 515 finding type errors, 545 finite tree type, 285 finite-state generating function, 294 first-class polymorphism, 340 fixed point, 142–145 combinator, 65 of a generating function, 282 theorem (Tarski-Knaster), 283 typing, using recursive
Data Mining: Concepts, Models, Methods, and Algorithms
by Mehmed Kantardzić · 2 Jan 2003 · 721pp · 197,134 words
mining. There have been many techniques used to model global or local temporal events. We will introduce only some of the most popular modeling techniques. Finite State Machine (FSM) has a set of states and a set of transitions. A state may have transitions to other states that are caused by fulfilling
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well when the transitions are not precise and does not scale well when the set of symbols for sequence representation is large. Figure 12.20. Finite-state machine. (a) State-transition table; (b) state-transition diagram. Markov Model (MM) extends the basic idea behind FSM. Both FSM and MM are directed graphs
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traditional algorithms for frequent itemsets detection. Counting serial itemsets, on the other hand, requires more computational resources. For example, unlike for parallel itemsets, we need finite-state automata to recognize serial episodes. More specifically, an appropriate l-state automaton can be used to recognize occurrences of an l-node serial sequence. For
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B A B C B A B A B B C B A C C}: (a) Find the longest subsequence with frequency ≥ 3. (b) Construct finite-state automaton (FSA) for the subsequence found in (a). 7. Find normalized contiguity matrix for the table of U.S. cities: Minneapolis Chicago New York Nashville
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