Agent verification is activity to gain assurances that purposeful artificial constructs act in accordance with their specifications. While primitive forms of inorganic agents have been used in manufacturing for centuries, the study of artificial agents did not begin until the mid 20th century. Foundational work on such agents was closely bound with the emergence of artificial intelligence as an academic discipline. Early agents deployed for industrial control systems and in computing were often controlled by quite simple logic however, not involving artificial intelligence as such. When deployed as part of a multi-agent system, even such simple agents could require special agent orientated testing methods, as their collective behaviour was challenging to verify with traditional testing techniques. Difficulties in providing assurances that agents will not behave in dangerous ways became more prevalent after the introduction of LLM agents, especially after the rapid acceleration of their deployment in 2025. The verification of agent behaviour can be conducted by formal or informal methods. Informal verification requires less mathematical skill. But when agents are part of systems where errors have significant risks — such as danger to human life, environmental damage or major financial loss — formal verification is preferred. Both regulators and system designers themselves like formal verification as it provides a high degree of mathematical certainty. It is not however always possible to formally test all aspects of an agent based system's behaviour, especially where newer LLM based agents are concerned, due in part to their high degree of autonomy. Accordingly, agent verification for low impact deployments might be carried out only with informal methods, while for high impact deployments, it may be performed with a mix of formal and informal techniques. == Terminology == In academia, the term agent verification is often defined to mean activity concerned with gaining assurance that the agent behaves in accordance with its specification - whether by processes such as testing or simulation. 'Verification' is typically contrasted with 'validation', the latter meaning activity concerned with checking that the specification itself meets user or real world needs. Such definitions are not universally adhered to however - for example, in some workplaces and documents, the words 'verification' and 'validation' can be used synonymously. Efforts to gain confidence in Agents have intensified sharply since 2025 due to the rapid roll out of LLM agents; different terms are sometimes used in the commercial sector. Here the term 'agent verification' can be used in the same sense as it is in academia, but sometimes the same activity can be covered by more ambiguous and wider ranging terms such as 'Agent governance' , 'Agent observability' or 'AI agent policing'. == History == === Classical agents === The theoretical underpinnings for artificial (inorganic) agents emerged in the mid 20th century, with establishment of cybernetics and artificial intelligence. Oliver Selfridge's 1958 Pandemonium - A Paradigm for Learning paper was an important early theoretical contribution in establishing agent oriented architecture. Practical implementations of agents for real world applications began to become widespread in the 1990s, after the introduction of the belief–desire–intention software model (BDI), and agent-oriented programming. Pure digital agents were deployed in computer infrastructure for purposes such as monitoring, while agents connected to real-world sensors and actuators were increasingly used in industrial control systems. While the concept of artificial agents was interwoven with early artificial intelligence studies right from the start, early agents lacked general purpose reasoning capabilities, often only having simple if then logic. Even a device as simple as a thermostat, which has a sensor and a means of acting, can be considered a proto agent in this sense. Verifying the behaviours of a simple single agent system is not generally especially difficult, but it can be a different matter when several simple agents coexist in the same system. Craig Reynolds's work on boids showed that relatively complex, "intelligent" behaviour can emerge from a number of such simple agents working together in a Multi-agent system (MAS). By the 1990s, even the behaviour of a single agent system could sometimes be quite complex; in accordance with the Belief–desire–intention software model, agents could have believes that might evolve over time. Agents were increasingly introduced that were controlled by quite large decision tree models, which had new vulnerabilities to adversarial attack. It was becoming increasingly apparent that traditional software verification methods had limitations for testing such agents, or even for the more primitive type of agents when they were deployed as part of a MAS. It was the use of agents for industrial control systems, sometimes associated with robotics, that lent urgency to the practice of agent verification. Informal testing might be acceptable for digital agents used say to monitor whether each of an organisation's computers are properly licensed. But with an increasing potential for faulty agents to result in a failure that might cause a large fire to break out at a chemical manufacturing plant, a botched medical operation, or even a crashed aircraft, the need to develop reliable means of verifying behaviour of such agents was considered urgent. The Foundation for Intelligent Physical Agents was established in 1996. From the late 90s, a growing number of industry and university based scientists began working on the problem, with researchers publishing papers on the verification of both single and multi agent systems. Much of this work showed how formal verification techniques like model checking could be used to gain a high level of assurance that agent based systems would conform with their specification. A 2018 systematic review covering 231 studies found that model checking was the most common technique for agent verification, with theorem proving the second most commonly used formal verification method. In the first two decades of the 20th century, agents run by AI became more common, with Siri and Alexa being well known examples. But such agents still lacked general reasoning capabilities and did not pose new pressing problems for agent verification. === General purpose reasoning agents === The advent of LLMs created huge potential for further use of artificial agents, as agents based on them could have general purpose cognitive abilities. Agents run by LLMs (and occasionally non-LLM foundation models) have similar vulnerability to adversarial attack as those run by decision tree models. The wider scope of actions for LLM agents has created new challenges for their verification, over and above those present for classical agents. For example, the LLM's neural network endows it with infinite domains, an especial challenge for traditional formal verification techniques. Academics began to study the problems involved in verifying LLM agents from 2018. Deployment of such agents began to accelerate in late 2023 after OpenAI's "function-calling" API was made available, and especially after Anthropic's late 2024 introduction of Model Context Protocol (MCP), a standardised way for LLM agents to gain contextual awareness, and to act on the world by calling various external tools. The rapid rollout of LLM agents following MCP's release has seen the task of agent verification receive increased attention within academia, and also from the private sector. In 2024 and 2025 several startups focusing on LLM agent verification have been founded in both Europe and the US to meet growing demand. == Approaches == === Formal verification === Formal verification involves proving the correctness of some or all aspects of a system using mathematical methods. Such methods can range from manual formal proof, to verification assisted with automated theorem provers like Isabelle. For agent verification, model checking is by far the most frequently used formal verification method; for pre-LLM models it was often complemented with techniques using computation tree logic. Another common method is theorem proving. Formal verification provides a higher degree of confidence than informal methods, but it is not always used, even when it is possible. Sometimes a person or organisation developing software agents won't have the necessary skills, or may not see it as worth the effort if the agent(s) will not have the ability to cause much harm even if they malfunction. When agents are deployed in systems where errors could have serious consequences, the ability of formal verification methods to provide mathematical certainty tends to be strongly preferred by both regulators and designers themselves. But even for high impact systems, formal verificatio
Identi.ca
identi.ca is a free and open-source social networking and blogging service based on the pump.io software, using the Activity Streams protocol. Identi.ca stopped accepting new registrations in 2013, but continues to operate alongside several other pump.io-based hosts provided by E14N which continue to accept new registrations. == Features == Identi.ca is similar to social networking sites like Facebook and Google+, allowing unlimited length status updates, rich text, and images. The Activity Streams protocol supports many kinds of activities such as games. OpenFarmGame is a prototype application for an Activity Streams-based game. Previous features from its StatusNet version such as hashtags, groups, and global search are not supported. == History == === StatusNet === The service received more than 8,000 registrations and 19,000 updates within the first 24 hours of publicly launching on July 2, 2008, and reached its 1,000,000th notice on November 4, 2008. In January 2009, identi.ca received investment funds from venture capital group Montreal Start Up. On March 30, 2009, Control Yourself (since renamed StatusNet Inc) announced that Identi.ca was to become part of a hosted microblogging service called status.net to be launched in May 2009. Status.net offers individual microblogs under a subdomain to be chosen by the customer. Identi.ca will remain a free service. All notices will be published under the Creative Commons Attribution 3.0 license by default, but paying customers will be free to choose a different license. Formerly based on StatusNet, a micro-blogging software package built on the OStatus specification (and earlier based on the OpenMicroBlogging specification), Identi.ca allowed users to send text updates (known as "notices") up to 140 characters long. While similar to Twitter in both concept and operation, Identi.ca/StatusNet provided many features not currently implemented by Twitter, including XMPP support and personal tag clouds. In addition, Identi.ca/StatusNet allowed free export and exchange of personal and "friend" data based on the FOAF standard; therefore, notices could be fed into a Twitter account or other service, and also ported in to a private system similar to Yammer. === pump.io === Developer Evan Prodromou chose to change the site to the pump.io software platform in development, because pump.io offers more features making it technically more advanced. Registration on Identi.ca was closed in December 2012 in preparation for the switch to pump.io software (the popularity of Identi.ca and "official" Status.net hosting were considered a hindrance to the creation of a federated social network). The conversion was completed on 12 July 2013. The 140 character per post limit was removed (in StatusNet, it was a setting, not an inherent limitation); now the blog posts can contain formatting and images. Groups, hashtags, and a page listing popular posts are not yet implemented in pump.io.
Best AI Image Generators in 2026
Comparing the best AI image generator? An AI image generator is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI image generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
AI Marketing Tools: Free vs Paid (2026)
Shopping for the best AI marketing tool? An AI marketing tool is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI marketing tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Probabilistic automaton
In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Markov chain and of a subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset. The number of stochastic languages is uncountable. The concept was introduced by Michael O. Rabin in 1963; a certain special case is sometimes known as the Rabin automaton (not to be confused with the subclass of ω-automata also referred to as Rabin automata). In recent years, a variant has been formulated in terms of quantum probabilities, the quantum finite automaton. == Informal Description == For a given initial state and input character, a deterministic finite automaton (DFA) has exactly one next state, and a nondeterministic finite automaton (NFA) has a set of next states. A probabilistic automaton (PA) instead has a weighted set (or vector) of next states, where the weights must sum to 1 and therefore can be interpreted as probabilities (making it a stochastic vector). The notions states and acceptance must also be modified to reflect the introduction of these weights. The state of the machine as a given step must now also be represented by a stochastic vector of states, and a state accepted if its total probability of being in an acceptance state exceeds some cut-off. A PA is in some sense a half-way step from deterministic to non-deterministic, as it allows a set of next states but with restrictions on their weights. However, this is somewhat misleading, as the PA utilizes the notion of the real numbers to define the weights, which is absent in the definition of both DFAs and NFAs. This additional freedom enables them to decide languages that are not regular, such as the p-adic languages with irrational parameters. As such, PAs are more powerful than both DFAs and NFAs (which are famously equally powerful). == Formal Definition == The probabilistic automaton may be defined as an extension of a nondeterministic finite automaton ( Q , Σ , δ , q 0 , F ) {\displaystyle (Q,\Sigma ,\delta ,q_{0},F)} , together with two probabilities: the probability P {\displaystyle P} of a particular state transition taking place, and with the initial state q 0 {\displaystyle q_{0}} replaced by a stochastic vector giving the probability of the automaton being in a given initial state. For the ordinary non-deterministic finite automaton, one has a finite set of states Q {\displaystyle Q} a finite set of input symbols Σ {\displaystyle \Sigma } a transition function δ : Q × Σ → ℘ ( Q ) {\displaystyle \delta :Q\times \Sigma \to \wp (Q)} a set of states F {\displaystyle F} distinguished as accepting (or final) states F ⊆ Q {\displaystyle F\subseteq Q} . Here, ℘ ( Q ) {\displaystyle \wp (Q)} denotes the power set of Q {\displaystyle Q} . By use of currying, the transition function δ : Q × Σ → ℘ ( Q ) {\displaystyle \delta :Q\times \Sigma \to \wp (Q)} of a non-deterministic finite automaton can be written as a membership function δ : Q × Σ × Q → { 0 , 1 } {\displaystyle \delta :Q\times \Sigma \times Q\to \{0,1\}} so that δ ( q , a , q ′ ) = 1 {\displaystyle \delta (q,a,q^{\prime })=1} if q ′ ∈ δ ( q , a ) {\displaystyle q^{\prime }\in \delta (q,a)} and 0 {\displaystyle 0} otherwise. The curried transition function can be understood to be a matrix with matrix entries [ θ a ] q q ′ = δ ( q , a , q ′ ) {\displaystyle \left[\theta _{a}\right]_{qq^{\prime }}=\delta (q,a,q^{\prime })} The matrix θ a {\displaystyle \theta _{a}} is then a square matrix, whose entries are zero or one, indicating whether a transition q → a q ′ {\displaystyle q{\stackrel {a}{\rightarrow }}q^{\prime }} is allowed by the NFA. Such a transition matrix is always defined for a non-deterministic finite automaton. The probabilistic automaton replaces these matrices by a family of right stochastic matrices P a {\displaystyle P_{a}} , for each symbol a in the alphabet Σ {\displaystyle \Sigma } so that the probability of a transition is given by [ P a ] q q ′ {\displaystyle \left[P_{a}\right]_{qq^{\prime }}} A state change from some state to any state must occur with probability one, of course, and so one must have ∑ q ′ [ P a ] q q ′ = 1 {\displaystyle \sum _{q^{\prime }}\left[P_{a}\right]_{qq^{\prime }}=1} for all input letters a {\displaystyle a} and internal states q {\displaystyle q} . The initial state of a probabilistic automaton is given by a row vector v {\displaystyle v} , whose components are the probabilities of the individual initial states q {\displaystyle q} , that add to 1: ∑ q [ v ] q = 1 {\displaystyle \sum _{q}\left[v\right]_{q}=1} The transition matrix acts on the right, so that the state of the probabilistic automaton, after consuming the input string a b c {\displaystyle abc} , would be v P a P b P c {\displaystyle vP_{a}P_{b}P_{c}} In particular, the state of a probabilistic automaton is always a stochastic vector, since the product of any two stochastic matrices is a stochastic matrix, and the product of a stochastic vector and a stochastic matrix is again a stochastic vector. This vector is sometimes called the distribution of states, emphasizing that it is a discrete probability distribution. Formally, the definition of a probabilistic automaton does not require the mechanics of the non-deterministic automaton, which may be dispensed with. Formally, a probabilistic automaton PA is defined as the tuple ( Q , Σ , P , v , F ) {\displaystyle (Q,\Sigma ,P,v,F)} . A Rabin automaton is one for which the initial distribution v {\displaystyle v} is a coordinate vector; that is, has zero for all but one entries, and the remaining entry being one. == Stochastic languages == The set of languages recognized by probabilistic automata are called stochastic languages. They include the regular languages as a subset. Let F = Q accept ⊆ Q {\displaystyle F=Q_{\text{accept}}\subseteq Q} be the set of "accepting" or "final" states of the automaton. By abuse of notation, Q accept {\displaystyle Q_{\text{accept}}} can also be understood to be the column vector that is the membership function for Q accept {\displaystyle Q_{\text{accept}}} ; that is, it has a 1 at the places corresponding to elements in Q accept {\displaystyle Q_{\text{accept}}} , and a zero otherwise. This vector may be contracted with the internal state probability, to form a scalar. The language recognized by a specific automaton is then defined as L η = { s ∈ Σ ∗ | v P s Q accept > η } {\displaystyle L_{\eta }=\{s\in \Sigma ^{}\vert vP_{s}Q_{\text{accept}}>\eta \}} where Σ ∗ {\displaystyle \Sigma ^{}} is the set of all strings in the alphabet Σ {\displaystyle \Sigma } (so that is the Kleene star). The language depends on the value of the cut-point η {\displaystyle \eta } , normally taken to be in the range 0 ≤ η < 1 {\displaystyle 0\leq \eta <1} . A language is called η-stochastic if and only if there exists some PA that recognizes the language, for fixed η {\displaystyle \eta } . A language is called stochastic if and only if there is some 0 ≤ η < 1 {\displaystyle 0\leq \eta <1} for which L η {\displaystyle L_{\eta }} is η-stochastic. A cut-point is said to be an isolated cut-point if and only if there exists a δ > 0 {\displaystyle \delta >0} such that | v P ( s ) Q accept − η | ≥ δ {\displaystyle \vert vP(s)Q_{\text{accept}}-\eta \vert \geq \delta } for all s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} == Properties == Every regular language is stochastic, and more strongly, every regular language is η-stochastic. A weak converse is that every 0-stochastic language is regular; however, the general converse does not hold: there are stochastic languages that are not regular. Every η-stochastic language is stochastic, for some 0 < η < 1 {\displaystyle 0<\eta <1} . Every stochastic language is representable by a Rabin automaton. If η {\displaystyle \eta } is an isolated cut-point, then L η {\displaystyle L_{\eta }} is a regular language. == p-adic languages == The p-adic languages provide an example of a stochastic language that is not regular, and also show that the number of stochastic languages is uncountable. A p-adic language is defined as the set of strings L η ( p ) = { n 1 n 2 n 3 … | 0 ≤ n k < p and 0. n 1 n 2 n 3 … > η } {\displaystyle L_{\eta }(p)=\{n_{1}n_{2}n_{3}\ldots \vert 0\leq n_{k}
GazoPa
GazoPa was an image search engine that used features from an image to search for and identify similar images which closed in 2011. GazoPa began in TechCrunch50 in 2008 before launching into a state of open beta in 2009. GazoPa branched out and released a flower photo community site called "GazoPa Bloom" in 2010. This site was for exploring flower images and, if users need help identifying a flower, uploading images for other people try to identify them. Both sites closed to the public in 2011 when the company decided to focus on other areas of their business.
Regular language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. == Formal definition == The collection of regular languages over an alphabet Σ is defined recursively as follows: The empty language ∅ is a regular language. For each a ∈ Σ (a belongs to Σ), the singleton language {a} is a regular language. If A is a regular language, A (Kleene star) is a regular language. Due to this, the empty string language {ε} is also regular. If A and B are regular languages, then A ∪ B (union) and A • B (concatenation) are regular languages. No other languages over Σ are regular. See Regular expression § Formal language theory for syntax and semantics of regular expressions. == Examples == All finite languages are regular; in particular the empty string language {ε} = ∅ is regular. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs. A simple example of a language that is not regular is the set of strings {anbn | n ≥ 0}. Intuitively, it cannot be recognized with a finite automaton, since a finite automaton has finite memory and it cannot remember the exact number of a's. Techniques to prove this fact rigorously are given below. == Equivalent formalisms == A regular language satisfies the following equivalent properties: it is the language of a regular expression (by the above definition) it is the language accepted by a nondeterministic finite automaton (NFA) it is the language accepted by a deterministic finite automaton (DFA) it can be generated by a regular grammar it is the language accepted by an alternating finite automaton it is the language accepted by a two-way finite automaton it can be generated by a prefix grammar it can be accepted by a read-only Turing machine it can be defined in monadic second-order logic (Büchi–Elgot–Trakhtenbrot theorem) it is recognized by some finite syntactic monoid M, meaning it is the preimage {w ∈ Σ | f(w) ∈ S} of a subset S of a finite monoid M under a monoid homomorphism f : Σ → M from the free monoid on its alphabet the number of equivalence classes of its syntactic congruence is finite. (This number equals the number of states of the minimal deterministic finite automaton accepting L.) Properties 10. and 11. are purely algebraic approaches to define regular languages; a similar set of statements can be formulated for a monoid M ⊆ Σ. In this case, equivalence over M leads to the concept of a recognizable language. Some authors use one of the above properties different from "1." as an alternative definition of regular languages. Some of the equivalences above, particularly those among the first four formalisms, are called Kleene's theorem in textbooks. Precisely which one (or which subset) is called such varies between authors. One textbook calls the equivalence of regular expressions and NFAs ("1." and "2." above) "Kleene's theorem". Another textbook calls the equivalence of regular expressions and DFAs ("1." and "3." above) "Kleene's theorem". Two other textbooks first prove the expressive equivalence of NFAs and DFAs ("2." and "3.") and then state "Kleene's theorem" as the equivalence between regular expressions and finite automata (the latter said to describe "recognizable languages"). A linguistically oriented text first equates regular grammars ("4." above) with DFAs and NFAs, calls the languages generated by (any of) these "regular", after which it introduces regular expressions which it terms to describe "rational languages", and finally states "Kleene's theorem" as the coincidence of regular and rational languages. Other authors simply define "rational expression" and "regular expressions" as synonymous and do the same with "rational languages" and "regular languages". Apparently, the term regular originates from a 1951 technical report where Kleene introduced regular events and explicitly welcomed "any suggestions as to a more descriptive term". Noam Chomsky, in his 1959 seminal article, used the term regular in a different meaning at first (referring to what is called Chomsky normal form today), but noticed that his finite state languages were equivalent to Kleene's regular events. == Closure properties == The regular languages are closed under various operations, that is, if the languages K and L are regular, so is the result of the following operations: the set-theoretic Boolean operations: union K ∪ L, intersection K ∩ L, and complement L, hence also relative complement K − L. the regular operations: K ∪ L, concatenation K ∘ L {\displaystyle K\circ L} , and Kleene star L. the trio operations: string homomorphism, inverse string homomorphism, and intersection with regular languages. As a consequence they are closed under arbitrary finite state transductions, like quotient K / L with a regular language. Even more, regular languages are closed under quotients with arbitrary languages: If L is regular then L / K is regular for any K. the reverse (or mirror image) LR. Given a nondeterministic finite automaton to recognize L, an automaton for LR can be obtained by reversing all transitions and interchanging starting and finishing states. This may result in multiple starting states; ε-transitions can be used to join them. == Decidability properties == Given two deterministic finite automata A and B, it is decidable whether they accept the same language. As a consequence, using the above closure properties, the following problems are also decidable for arbitrarily given deterministic finite automata A and B, with accepted languages LA and LB, respectively: Containment: is LA ⊆ LB ? Disjointness: is LA ∩ LB = {} ? Emptiness: is LA = {} ? Universality: is LA = Σ ? Membership: given a ∈ Σ, is a ∈ LB ? For regular expressions, the universality problem is NP-complete already for a singleton alphabet. For larger alphabets, that problem is PSPACE-complete. If regular expressions are extended to allow also a squaring operator, with "A2" denoting the same as "AA", still just regular languages can be described, but the universality problem has an exponential space lower bound, and is in fact complete for exponential space with respect to polynomial-time reduction. For a fixed finite alphabet, the theory of the set of all languages – together with strings, membership of a string in a language, and for each character, a function to append the character to a string (and no other operations) – is decidable, and its minimal elementary substructure consists precisely of regular languages. For a binary alphabet, the theory is called S2S. == Complexity results == In computational complexity theory, the complexity class of all regular languages is sometimes referred to as REGULAR or REG and equals DSPACE(O(1)), the decision problems that can be solved in constant space (the space used is independent of the input size). REGULAR ≠ AC0, since it (trivially) contains the parity problem of determining whether the number of 1 bits in the input is even or odd and this problem is not in AC0. On the other hand, REGULAR does not contain AC0, because the nonregular language of palindromes, or the nonregular language { 0 n 1 n : n ∈ N } {\displaystyle \{0^{n}1^{n}:n\in \mathbb {N} \}} can both be recognized in AC0. If a language is not regular, it requires a machine with at least Ω(log log n) space to recognize (where n is the input size). In other words, DSPACE(o(log log n)) equals the class of regular languages. In practice, most nonregular problems are studied in a setting with at least logarithmic space, as this is the amount of space required to store a pointer into the input tape. == Location in the Chomsky hierarchy == To locate the regular languages in the Chomsky hierarchy, one notices that every regular language is context-free. The converse is not true: for example, the language consisting of all strings having the same number of as as bs is context-free but not regular. To prove that a language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma. Other approaches include using the closure properties of regular languages or quantifying Kolmogorov complexity. Important subclasses of regular languages include: Finite languages, those containing only a finite number of words. These are regular la