Found inside – Page 110In particular, it is well known that the generalized word problem for finitely presented groups with decidable word problem is in general undecidable. Found inside – Page 283... due to the problem of state explosion, and they do not provide any insight ... for efficiency reasons, also be useful when tackling decidable problems. Found inside – Page 124... all lead to the class of recursive sets, mathematicians generally accept the notion of recursive set as the precise definition of a decidable problem. Found inside – Page 201Examples of groups G where the Generalized Word Problem is decidable include ... Problem is undecidable, but the Cyclic Membership Problem is easy. Found inside – Page 80The polynomial hierarchy classifies a subclass of all decidable problems, imely those that are NP-hard. A problem is called NP-hard if any other 'oblem in ... Found inside – Page 5Turing introduced the latter with the goal of classifying undecidable problems but his ideas eventually translated into a classification of decidable ... Found inside – Page 69Recently [47], the simulation preorder/equivalence problem between a BPA/PDA ... Of course, some of the generally undecidable problems become decidable when ... Found inside – Page 126(ii) The inclusion problem for simple languages (s-languages) is undecidable but the equivalence problem is decidable, [5]. (iii) The inclusion problem for ... Found inside – Page 150(b) Finite state automata (FSA) has no undecidability CFL membership problem is also decidable. So option (b) i.e Ambiguity of CFL cannot be decidable. 58. Found inside – Page 437Decidable problems may be classified according to the computational resources required to decide them. Important complexity classes are: NLogSpace, ... Found inside – Page 335There is a third type of problem that can be handled by a Turing machine. These are decidable problems.A decidable problem is one where a problem is posed ... Found inside – Page 130We exhibit some decidable cases and some undecidable ones. ... 7.1 Some Decidable Problems We start by consider properties of the simple form α = ♢A. We ... Found inside – Page 193How do we express that a problem is decidable? If the problem P(x) is a predicate on a set A, then Hopcroft and Ullman use the idea that a function f from A ... Found inside – Page 133Problem. for. Computational. Models: Decidable. and. Undecidable. Cases. Vladimir A. Zakharov Faculty of Computational Mathematics and Cybernetics, ... Found inside – Page 90We illustrate our purpose with many examples of decidable problems on ... in Chapters 9 and 10 in the context of the domino problem and of Wang tiles. Found inside – Page 9emptiness problem of acyclic extended S[pr1 ,pr2]-automata is equivalent to the ... Hence, by Theorem7, the emptiness problem is decidable for acyclic ... Found inside – Page 201checking problem for finite state programs is recast in terms of testing ... many decision problems with respect to Petri nets are known to be decidable. Found inside – Page 75Definition: Decidable, semi-decidable Let L be a language. • L is called decidable, if there is a TM M which stops on all inputs and accepts an input x iff ... Found inside – Page 499It means that for a decidable problem there must exist a TM. Decidable problems are called solvable problems which can be solved by the computer. Found inside – Page 8Even with this modern reformulation Lusin's problem was in fact completely settled by the works of Stern ([25], [26) and Sami ([23]), from which it follows ... Found inside – Page 66It is undecidable for 3-state N-automata A whether A has indistinguishable words u and v. 3.4 Generalized Word Problem In the generalized word problem for a ... Found inside – Page 98In general this problem is totally undecidable. We shall show, however, that in numerous practical cases it can be reduced to decidable problems of ... Found inside – Page 84Some problems are decidable but undecidability comes fast into the picture. Even considering polynomial systems yields many undecidable problems: [10] for ... Found inside – Page 67The choosing of which pj to make true is a subtle (though typically decidable) problem, and the agent will take into account several factors, ... Found inside – Page 356RICE'S THEOREM AND MORE UNDECIDABLE PROBLEMS A problem that can be answered yes or no is said to be a decision problem . ' For example , ( i ) given a ... Found inside – Page 104Determining the validity of arguments in sentence logic, for example, is a decidable problem. Interestingly, in a discussion of this notion, Alonzo Church ... Found inside – Page 183... these are in some sense more “expensive” resources than states and transitions, since most decidable problems concerning timed automata have worst-case ... Found inside – Page 148Problem A decider transformer Problem B decider Yes Yes No No Figure 6.6 ... In that case , it must be the case that Problem B is also undecidable . Found inside – Page 347... propositional logic LR(k) language 105 LR(l) 105 membership problem for ... decidable problem, decision problem, halting problem, membership problem, ... Found inside – Page 37This proposition holds for the problem in all generality. ... It is known that (PCP2) is decidable and that (PCPk) is undecidable for k ⩾ 7 . Found inside – Page 115... the problem A if C accepts all m that belong to A and rejects all m that do not belong to A. Let S denote class of problems decidable by an RBS program. Found inside – Page 88It has a decidable model-checking problem, but an undecidable satisfiability problem. In this, it is similar to first-order logic. The decidability of model ... Found inside – Page 4Parameterized verification problems for our model can be defined by considering the ... The problem easily gets undecidable since for parametric initial ... Found insidethe equivalence (*) gives a reduction of the problem 'x ∈ W x ' to the problem 'σ is valid'. Hence the latter is undecidable. Found inside – Page 304Theorem 12.2 If the halting problem were decidable , then every recursively enumerable language would be recursive . Consequently , the halting problem is ... Found inside – Page 289Then (i) the divisibility problem for Inv < X; R → is decidable if and only if it is decidable, for every e,fe E[FIM(X)], whether or not (e, f) e R'; ... Found inside – Page 403The first ones were undecidable problems. These problems are called “undecidable” because it can be proven that algorithms that solve them cannot exist. Found inside – Page 66There is no smallest variety of relation algebras with an undecidable equational theory. PROBLEM 3.6. Does the lattice of varieties of relation algebras ... Found inside – Page 240The semilinear reachability problem for VASS is decidable. ... the bond-type reachability problem is undecidable, as shown in Theorem 5. Found inside – Page ivThus they can describe various problems which cannot be ... We also discuss the possibility that certain decidable problems require enormous amount of time ... Found inside – Page 31.1 Problems and Complexity 1.1.1 Problems: Well-Defined (Simple), Ill-Defined (Complex), and Non-Defined (Undecidable) Broadly, decidable problems are of ... Found inside – Page 405Clearly, any decidable problem is also semidecidable, while the converse does not ... decidability problems for (input-driven) (finite-turn) queue automata. Found inside – Page 15u, v e A* represent the same element in the semigroup defined by P. If such an algorithm exists, we say that the word problem is decidable, otherwise it is ... Found inside – Page 311Definition 10.4 A problem/language is undecidable if it is not decidable. Note: A decidable problem is called a solvable problem and an undecidable problem ... Found inside – Page 413... of results about the complexity of decision problems for various questions ... analysis of systems The border between undecidable and decidable problems ... Found insideArnon (1979) has noted that testing adjacency is a decidable problem. To see this, we simply have to show a Tarski formula saying that byc ... Found inside – Page 1233The PCMP is known to be undecidable for arbitrary systems [6]. However, restrictions can be imposed on the systems leading to decidable problems; ... Found inside – Page 587Note that the above problem is undecidable when both h and g are nondeterministic gsm ... Then the commutation problem is decidable for L if and only if the ... Found inside – Page 492Since the conjugacy problem is decidable for one - relator groups with torsione , from Theorem 4.3 there follows Corollary 4.4 ( [ 30 ] ) The conjugacy ... 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