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Movie Title Year Distributor Notes Rev Formats Black and Stacked 2 2005 Score MastOnly 1 DRO Diana und Team im Sexrausch 2002 DBM Video O Fotzenboutique Intim 2002 Puaka LezOnly Goren auf dem Gipfel 2003 Videorama Kuschel Titten 10 2002 Multi Media Verlag Kuschel Titten 6 2002 Multi Media Verlag Bald Madchen vom Immenhof 2002 Multi Media Verlag Miss Donnerbusen 4 2002 Multi Media Verlag Mosen-Casting 2002 XXL Bald Perverse Nachbarn 2002 XXL Facial Bald Schlampen 2 2002 Multi Media Verlag Bald Schmutzige Spiele im Swinger Club 2002 Multi Media Verlag Facial Bald Stacked and Packed 3 2004 Score MastOnly DRO Tittenschwingen extrem 2002 Puaka Bald Traumurlaub - Chaos inklusive 2003 Videorama Facial Voluptuous Xtra 5 2002 Score 1 state. This acceptor will finish in an accept state, if the binary string contains an even number of 0s (including any binary string containing no 0s). Examples of strings accepted by this acceptor are e (the empty string), 1, 11, 11..., 00, 010, 1010, 10110, etc.
Classifiers Classifiers are a generalization of acceptors that produce n-ary output where n is strictly greater than two.[citation needed] Transducers Main article: Finite-state transducer Fig. 6 Transducer FSM: Moore model example Fig. 7 Transducer FSM: Mealy model example Transducers produce output based on a given input and/or a state using actions. They are used for control applications and in the field of computational linguistics. In control applications, two types are distinguished: Moore machine The FSM uses only entry actions, i.e., output depends only on state. The advantage of the Moore model is a simplification of the behaviour. Consider an elevator door. The state machine recognizes two commands: "command_open" and "command_close", which trigger state changes. The entry action (E:) in state "Opening" starts a motor opening the door, the entry action in state "Closing" starts a motor in the other direction closing the door. States "Opened" and "Closed" stop the motor when fully opened or closed. They signal to the outside world (e.g., to other state machines) the situation: "door is open" or "door is closed". Mealy machine The FSM also uses input actions, i.e., output depends on input and state. The use of a Mealy FSM leads often to a reduction of the number of states. The example in figure 7 shows a Mealy FSM implementing the same behaviour as in the Moore example (the behaviour depends on the implemented FSM execution model and will work, e.g., for virtual FSM but not for event-driven FSM). There are two input actions (I:): "start motor to close the door if command_close arrives" and "start motor in the other direction to open the door if command_open arrives". The "opening" and "closing" intermediate states are not shown.

Sequencers Sequencers (also called generators) are a subclass of acceptors and transducers that have a single-letter input alphabet. They produce only one sequence which can be seen as an output sequence of acceptor or transducer outputs.[6] Determinism A further distinction is between deterministic (DFA) and non-deterministic (NFA, GNFA) automata. In a deterministic automaton, every state has exactly one transition for each possible input. In a non-deterministic automaton, an input can lead to one, more than one, or no transition for a given state. The powerset construction algorithm can transform any nondeterministic automaton into a (usually more complex) deterministic automaton with identical functionality. A finite-state machine with only one state is called a "combinatorial FSM". It only allows actions upon transition into a state. This concept is useful in cases where a number of finite-state machines are required to work together, and when it is convenient to consider a purely combinatorial part as a form of FSM to suit the design tools.[10] Alternative semantics There are other sets of semantics available to represent state machines. For example, there are tools for modeling and designing logic for embedded controllers.[11] They combine hierarchical state machines (which usually have more than one current state), flow graphs, and truth tables into one language, resulting in a different formalism and set of semantics.[12] These charts, like Harel's original state machines,[13] support hierarchically nested states, orthogonal regions, state actions, and transition actions.[14] Mathematical model In accordance with the general classification, the following formal definitions are found. A deterministic finite-state machine or deterministic finite-state acceptor is a quintuple {\displaystyle (\Sigma ,S,s_{0},\delta ,F)}(\Sigma ,S,s_{0},\delta ,F), where: {\displaystyle \Sigma }\Sigma is the input alphabet (a finite non-empty set of symbols); {\displaystyle S}S is a finite non-empty set of states; {\displaystyle s_{0}}s_{0} is an initial state, an element of {\displaystyle S}S; {\displaystyle \delta }\delta is the state-transition function: {\displaystyle \delta :S\times \Sigma \rightarrow S}\delta :S\times \Sigma \rightarrow S (in a nondeterministic finite automaton it would be {\displaystyle \delta :S\times \Sigma \rightarrow {\mathcal {P}}(S)}\delta :S\times \Sigma \rightarrow {\mathcal {P}}(S), i.e. {\displaystyle \delta }\delta would return a set of states); {\displaystyle F}F is the set of final states, a (possibly empty) subset of {\displaystyle S}S. For both deterministic and non-deterministic FSMs, it is conventional to allow {\displaystyle \delta }\delta to be a partial function, i.e. {\displaystyle \delta (s,x)}{\displaystyle \delta (s,x)} does not have to be defined for every combination of {\displaystyle s\in S}{\displaystyle s\in S} and {\displaystyle x\in \Sigma }x\in \Sigma . If an FSM {\displaystyle M}M is in a state {\displaystyle s}s, the next symbol is {\displaystyle x}x and {\displaystyle \delta (s,x)}{\displaystyle \delta (s,x)} is not defined, then {\displaystyle M}M can announce an error (i.e. reject the input). This is useful in definitions of general state machines, but less useful when transforming the machine. Some algorithms in their default form may require total functions. A finite-state machine has the same computational power as a Turing machine that is restricted such that its head may only perform "read" operations, and always has to move from left to right. That is, each formal language accepted by a finite-state machine is accepted by such a kind of restricted Turing machine, and vice versa.[15] A finite-state transducer is a sextuple {\displaystyle (\Sigma ,\Gamma ,S,s_{0},\delta ,\omega )}(\Sigma ,\Gamma ,S,s_{0},\delta ,\omega ), where: {\displaystyle \Sigma }\Sigma is the input alphabet (a finite non-empty set of symbols); {\displaystyle \Gamma }\Gamma is the output alphabet (a finite non-empty set of symbols); {\displaystyle S}S is a finite non-empty set of states; {\displaystyle s_{0}}s_{0} is the initial state, an element of {\displaystyle S}S; {\displaystyle \delta }\delta is the state-transition function: {\displaystyle \delta :S\times \Sigma \rightarrow S}\delta :S\times \Sigma \rightarrow S; {\displaystyle \omega }\omega is the output function. If the output function depends on the state and input symbol ({\displaystyle \omega :S\times \Sigma \rightarrow \Gamma }\omega :S\times \Sigma \rightarrow \Gamma ) that definition corresponds to the Mealy model, and can be modelled as a Mealy machine. If the output function depends only on the state ({\displaystyle \omega :S\rightarrow \Gamma }\omega :S\rightarrow \Gamma ) that definition corresponds to the Moore model, and can be modelled as a Moore machine. A finite-state machine with no output function at all is known as a semiautomaton or transition system. If we disregard the first output symbol of a Moore machine, {\displaystyle \omega (s_{0})}{\displaystyle \omega (s_{0})}, then it can be readily converted to an output-equivalent Mealy machine by setting the output function of every Mealy transition (i.e. labeling every edge) with the output symbol given of the destination Moore state. The converse transformation is less straightforward because a Mealy machine state may have different output labels on its incoming transitions (edges). Every such state needs to be split in multiple Moore machine states, one for every incident output symbol.[16] Optimization Main article: DFA minimization Optimizing an FSM means finding a machine with the minimum number of states that performs the same function. The fastest known algorithm doing this is the Hopcroft minimization algorithm.[17][18] Other techniques include using an implication table, or the Moore reduction procedure. Additionally, acyclic FSAs can be minimized in linear time.[19] Implementation Hardware applications Fig. 9 The circuit diagram for a 4-bit TTL counter, a type of state machine In a digital circuit, an FSM may be built using a programmable logic device, a programmable logic controller, logic gates and flip flops or relays. More specifically, a hardware implementation requires a register to store state variables, a block of combinational logic that determines the state transition, and a second block of combinational logic that determines the output of an FSM. One of the classic hardware implementations is the Richards controller. In a Medvedev machine, the output is directly connected to the state flip-flops minimizing the time delay between flip-flops and output.[20][21] Through state encoding for low power state machines may be optimized to minimize power consumption. Software applications The following concepts are commonly used to build software applications with finite-state machines: Automata-based programming Event-driven finite-state machine Virtual finite-state machine State design pattern Finite-state machines and compilers Finite automata are often used in the frontend of programming language compilers. Such a frontend may comprise several finite-state machines that implement a lexical analyzer and a parser. Starting from a sequence of characters, the lexical analyzer builds a sequence of language tokens (such as reserved words, literals, and identifiers) from which the parser builds a syntax tree. The lexical analyzer and the parser handle the regular and context-free parts of the programming language's grammar

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