Joseph S. Ullian’s research while affiliated with Washington University in St. Louis and other places

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Publications (9)


Three theorems concerning principal AFLs
  • Article

June 1971

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5 Reads

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14 Citations

Journal of Computer and System Sciences

J.S. Ullian

(1)If every set in ℒ is a subset of a* and the empty word belongs to one of them, then Figure optionsView in workspaceDownload full-size imageDownload as PowerPoint slide. One consequence is that Figure optionsView in workspaceDownload full-size imageDownload as PowerPoint slide is always principal for Figure optionsView in workspaceDownload full-size imageDownload as PowerPoint slide.(2)On the other hand, there is a language Figure optionsView in workspaceDownload full-size imageDownload as PowerPoint slide such that Figure optionsView in workspaceDownload full-size imageDownload as PowerPoint slide


Three Theorems on Abstract Families of Languages

January 1970

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5 Reads

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16 Citations

(1) If every set in @@@@ is a subset of a* and the empty word belongs to one of them, then 7(@@@@)&equil;&7circ; (@@@@). One consequence is that &7circ;(L) is always principal for L ≤ a*. (2) On the other hand, there is a language L ≤ a*b* such that &7circ;(L) is not principal. (3) There are subsets J and K of a* such that 7(J) @@@@ 7(K) is not principal.


The Inherent Ambiguity Partial Algorithm Problem for Context Free Languages

January 1969

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5 Reads

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1 Citation

It is shown that there is no “partial algorithm” (effective procedure that may fail to terminate) by which, given a context free grammar, one can always find an unambiguous context free grammar generating the same language if such an unambiguous grammar exists. The argument turns on the degree of unsolvability of the inherent ambiguity problem for context free languages.


Partial Algorithm Problems for Context Free Languages

July 1967

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15 Reads

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27 Citations

Information and Control

By “grammar≓ we mean context free grammar; when G is a grammar, L(G) is the language generated by G. Suppose a “birdy≓ tells us of a given grammar G that there is a finite automaton accepting exactly the words in L(G). Can such an automaton be found? We understand this question (due to Ginsburg) as asking if there is an effective operator\3-a “partial algorithm≓\3-applicable to grammars and suitably defined for each grammar that generates a regular set. How the operator is to behave when applied to other grammars is not specified. We show that there is no such partial algorithm by constructing a class of grammars Gn such that (i) for every n, L(Gn) lacks at most one of the words over its alphabet and (ii) the set of n for which L(Gn) contains every one of its alphabet's words is non-recursive. With the aid of like constructions we are able to answer questions of Ginsburg and Rose: On each of four construals, there is no partial algorithm for identifying, given grammars G1 and G2, a sequential machine, if one exists, mapping L(G1) to L(G2). Obtain the four construals by taking “sequential machine≓ as either “generalized sequential machine≓ or “complete sequential machine≓, and “mapping to≓ as either “mapping onto≓ or “mapping onto an infinite subset of≓. Further partial algorithm problems are resolved, some of them concerning such families as bounded languages and sequences. We include several observations on the relationship between partial algorithm and associated decision problems.


The Independence of Inherent Ambiguity From Complementedness Among Context-Free Languages

October 1966

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9 Reads

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12 Citations

Journal of the ACM

Call a (context-free) language unambiguous if it is not inherently ambiguous. In the absence of evidence to the contrary, the suspicion has arisen that the unambiguous languages might be precisely those languages with context-free complements. The two theorems presented in this paper lay the suspicion to rest by providing (1) an inherently ambiguous language with context-free complement and (2) an unambiguous language without context-free complement. This establishes the independence of inherent ambiguity from complementedness among the context-free languages.


Preservation of unambiguity and inherent ambiguity in context-free languages

July 1966

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12 Reads

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19 Citations

Journal of the ACM

Various elementary operations are studied to find whether they preserve on ambiguity and inherent ambiguity of language (“language” means “context-free language”) The following results are established: If L is an unambiguous language and S is a generalized sequential machine, then (a) S ( L ) is an unambiguous language if S is one-to-one on L , and (b) S ⁻¹ ( L ) is an unambiguous language. Inherent ambiguity is preserved by every generalized sequential machine which is one-to-one on the set of all words. The product (either left or right) of a language and a word preserves both unambiguity and inherent ambiguity. Neither unambiguity nor inherent ambiguity is preserved by any of the following language preserving operations: (a) one state complete sequential machine; (b) product by a two-element set; (c) Init ( L ) = [ u ≠ dur in L for some v ]; (d) Subw ( L ) = [ w ≠ durr in L for some u , v ].


Failure of a Conjecture About Context Free Languages

February 1966

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7 Reads

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2 Citations

Information and Control

For a set L of words over an alphabet lacking the letter c, let N(L) = {xcy | x, y in L Λ x ≠ y}. Haines has shown that if L is regular, N(L) is context free. The converse has been widely conjectured. If true, it would allegedly support a neat argument to show that English is not context free. The failure of the conjecture is established by showing N(L) context free for the nonregular set L = {aibidk | i ≠ j V j ≠ k}ce:italic>.


Ambiguity in context free languages

January 1966

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9 Reads

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118 Citations

Journal of the ACM

Four principal results about ambiguity in languages (i.e., context free languages) are proved. It is first shown that the problem of determining whether an arbitrary language is inherently ambiguous is recursively unsolvable. Then a decision procedure is presented for determining whether an arbitrary bounded grammar is ambiguous. Next, a necessary and sufficient algebraic condition is given for a bounded language to be inherently ambiguous. Finally, it is shown that no language contained in w1*w2*, each w1 a word, is inherently ambiguous.


Citations (7)


... From [14] we know, that, in general, principality of trios is not preserved under intersection. ...

Reference:

On the intersection of stacks and queues
Three theorems concerning principal AFLs
  • Citing Article
  • June 1971

Journal of Computer and System Sciences

... Proving that a language is inherently ambiguous is a difficult question, as it is an impossibility notion, and it is undecidable in general [14,15]. In practice, three different methods have emerged to prove the inherent ambiguity of some context-free languages: an approach based on iterations on derivation trees [25,26], an other based on iterations on semilinear sets [14,16,29], and finally an approach based on generating series [10,17,21,28]. The first two approaches are best suited for (and for the second, limited to) bounded languages. ...

The Independence of Inherent Ambiguity From Complementedness Among Context-Free Languages
  • Citing Article
  • October 1966

Journal of the ACM

... Ces langages sont très intéressants pour comprendre les limites d'expressivité du modèle étudié, et séparer la classe générale de sa sous-classe non ambiguë. Malheureusement, pour de nombreux modèles (comme les langages algébriques ou les langages reconnus par des automates de Parikh), décider l'intrinsèque ambiguïté d'un langage est indécidable [10,2]. ...

Ambiguity in context free languages
  • Citing Article
  • January 1966

Journal of the ACM

... We conjecture that the answer to this problem is negative. An approach may be to reduce the problem to a so called "birdie problem" [30] (cf also [16], Ch. 8). In such a problem, assuming the feasibility of the computation of the Zariski closure of the groups above, one gets, as a consequence, the decidability of some unsolvable problem. ...

Partial Algorithm Problems for Context Free Languages
  • Citing Article
  • July 1967

Information and Control

... The natural conjecture is that all xy languages with strictly CF bases fail to be CF. Unfortunately, Ullian (1966) has shown that this is not so; the language L' = {aibJdk; i --/: j or j ~ k} is strictly CF, but Ullian shows that the xy language {xcy; x, y ~ L', x ~ y} is CF. Nevertheless, it is clear that there are infinitely many non-CF xy languages. ...

Failure of a Conjecture About Context Free Languages
  • Citing Article
  • February 1966

Information and Control