Document:

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                                                                    EXHIBIT 10.9

                           NON-COMPETITION AGREEMENT

     THIS NON-COMPETITION AGREEMENT (the "Agreement") is entered into as of
January 1, 2000 by and among Numerical Technologies, Inc., a California
corporation ("Parent"), Transcription Enterprises, Inc., a Delaware corporation
and a wholly owned subsidiary of Parent ("Sub"), Transcription Enterprises
Limited, a California corporation (the "Company") and Roger Sturgeon (the
"Executive").

                                   Background
                                   ----------

     A.  Parent, Sub, the Company, Messrs. Kevin MacLean and Roger Sturgeon
have entered into an Agreement and Plan of Reorganization dated as of December
21, 1999 (the "Reorganization Agreement"), which provides for the merger (the
"Merger") of the Company with and into Sub.  Capitalized terms not otherwise
defined in this Agreement have the meanings defined for them in the
Reorganization Agreement.

     B.  As a condition to the Merger, to preserve the value of the business
being acquired by Parent, the Reorganization Agreement contemplates, among other
things, that the Executive enter into this Agreement effective upon the
Effective Time of the Merger.

     NOW THEREFORE, in consideration of the mutual promises made in this
Agreement, Parent, the Company and the Executive agree as follows:

     1.  Covenant Not to Compete or Solicit.
         ----------------------------------

         (a)  For two (2) years after the termination of Executive's employment
with the Surviving Corporation, Parent or any subsidiary thereof (the "Non-
Compete Period"), the Executive shall not directly or indirectly for himself or
on behalf of or in conjunction with any other person, company, partnership,
corporation, business, group or other entity, without the prior written consent
of Parent, engage anywhere in the world in (whether as an employee, consultant,
proprietor, partner, director or otherwise), or have any ownership interest in
(except for ownership of one percent (1%) or less of the outstanding securities
of an entity whose securities are listed on a national securities exchange), or
participate in the financing, operation, management or control of, any firm,
corporation or business or any business unit of any firm or corporation in any
business selling products or services in direct competition with Parent's or the
Surviving Corporation's business of developing, marketing, maintaining,
supporting or servicing of layout design, mask manufacturing, inspection and
direct-write-on-wafer data preparation software or software applications and
services that enable integrated circuit designers and manufacturers to produce
ICs with subwavelength feature sizes (the "Competing Business"), provided that
                                                                 --------
this Section 1(a) shall not be applicable to the Executive's participation as a
service provider in any division of a firm or corporation which division and
Executive's participation in such division does not relate in any way to the
Competing Business.
<PAGE>

     During the Non-Compete Period, the Executive shall not, directly or
indirectly, without the prior written consent of Parent, (i) solicit, encourage
or take any other action which is intended to induce any employee of the
Surviving Corporation or Parent or any subsidiary thereof to terminate his or
her employment with the Surviving Corporation or Parent or any subsidiary
thereof (as the case may be), or (ii) interfere in any manner with the
contractual or employment relationship between the Surviving Corporation and any
employee of the Surviving Corporation or Parent and any employee of Parent or
any subsidiary of the Surviving Corporation or Parent and any employee of any
such subsidiary (collectively, the "Solicitation Restriction"). Notwithstanding
any other provisions contained herein to the contrary, (i) the last day of the
Non-Compete Period shall in no event be later than the third anniversary of the
effective date of the Merger and (ii) this Agreement shall not be applicable
with respect to the Solicitation Restriction or the Executive's participation as
a service provider or holding an equity interest in any successor entity of the
Company or an entity to which all or substantially all of the assets of the
Company is transferred provided that (a) an Event of Default (as defined in
Section 5 of the Promissory Notes issued pursuant to the Reorganization
Agreement) has occurred and is continuing and (b) the Executive has sought
enforcement of the Security Agreement relating to the Promissory Note held by
Executive. The parties acknowledge that Executive owns certain equity interest
as of the date hereof in Rave, Inc., a corporation not involving a Competing
Business.

          (b) The covenants contained in the preceding paragraphs shall be
construed as a series of separate covenants, one of each county, city and state
of any geographic area where any business is presently carried on by Parent, the
Surviving Corporation or the Company.  Except for geographic coverage, each such
separate covenant shall be identical in terms to the covenant contained in the
preceding paragraphs.  If, in any judicial proceeding, a court refuses to
enforce any of such separate covenants (or any part thereof), then such
unenforceable covenant (or such part) shall be eliminated from this Agreement to
the extent necessary to permit the remaining separate covenants (or portions
thereof) to be enforced.  In the event that the provisions of this Section 1 are
deemed to exceed the time, geographic or scope limitations permitted by
applicable law, then such provisions shall be reformed to the maximum time,
geographic or scope limitations, as the case may be, permitted by applicable
laws.

          (c) The Executive acknowledges that the Executive's covenant not to
compete or solicit contained in this Section 1 is a condition precedent to the
Merger to preserve the value of the business being purchased by Parent pursuant
to the Merger.  The Executive further acknowledges that breach of this Section 1
would cause irreparable injury to Parent and the Surviving Corporation and
agrees that in the event of such breach, Parent and the Surviving Corporation
shall each be entitled to seek injunctive relief without the necessity of
proving actual damages.

     2.   Miscellaneous.
          -------------

          (a) Severability.  If any portion of this Agreement is held by a court
              ------------
of competent jurisdiction to conflict with any federal, state or local law, such
portion of this Agreement shall be of no force or effect and this Agreement
shall otherwise remain in full force and effect and be construed as if such
portion had not been included in this Agreement.

                                      -2-
<PAGE>

          (b) No Assignment.  The Executive shall not assign this Agreement or
              -------------
any rights or obligations under this Agreement without the prior written consent
of Parent.

          (c) Notice.  Any notice or other communication required or permitted
              ------
under this Agreement shall be made in writing and delivered personally to the
other parties or sent by certified or registered mail, return receipt requested
and postage prepaid to the addresses set forth on the signature page hereto or
such other address as any such party shall have furnished to the other parties
in writing in accordance with this Section 2(c).

          (d) Entire Agreement.  This Agreement contains the entire agreement
              ----------------
and understanding of the parties and supersedes all prior discussions,
agreements and understandings relating to the subject matter of this Agreement.
This Agreement may not be changed or modified, except by an agreement in writing
executed by Parent and the Executive.

          (e) Effectiveness: Term.  This Agreement shall become effective upon
              -------------------
the Effective Date and shall continue in full force and effect for three (3)
years from its effectiveness.

          (f) Other.  The waiver of a breach of any term or provision of this
              -----
Agreement shall not operate as or be construed to be a waiver of any other
previous or subsequent breach of this Agreement.  This Agreement shall be
governed by the laws of the State of California.  All captions and section
headings used in this Agreement are for convenient reference only and do not
form a part of this Agreement.  This Agreement may be executed in counterparts,
and each counterpart shall have the same force and effect as an original and
shall constitute an effective, binding agreement on the part of each of the
undersigned.

                                      -3-
<PAGE>

     IN WITNESS WHEREOF, the parties have executed this Agreement as of the date
first above written above.

NUMERICAL TECHNOLOGIES, INC.           EXECUTIVE

By: /s/ Yagyensh C. Pati               /s/ Roger Sturgeon
   ---------------------------         ---------------------------
   Name:                               Name:
   Title:                              Address:
   Address:

TRANSCRIPTION ENTERPRISES LIMITED

By: /s/ Kevin MacLean
   ---------------------------
   Name:     Kevin MacLean
   Title:    Secretary, Vice President
   Address:  18990 Overlook Rd.
             Los Gatos, CA 99030

TRANSCRIPTION ENTERPRISES, INC.

By: /s/ Yagyensh C. Pati
   ---------------------------
   Name:
   Title:
   Address:

                 [Signature Page to Non-Competition Agreement]<PAGE>

                                                                   EXHIBIT 10.10

                           NON-COMPETITION AGREEMENT

     THIS NON-COMPETITION AGREEMENT (the "Agreement") is entered into as of
January 1, 2000 by and among Numerical Technologies, Inc., a California
corporation ("Parent"), Transcription Enterprises, Inc., a Delaware corporation
and a wholly owned subsidiary of Parent ("Sub"), Transcription Enterprises
Limited, a California corporation (the "Company") and Kevin MacLean (the
"Executive").

                                  Background
                                  ----------

     A.  Parent, Sub, the Company, Messrs. Kevin MacLean and Roger Sturgeon have
entered into an Agreement and Plan of Reorganization dated as of December 21,
1999 (the "Reorganization Agreement"), which provides for the merger (the
"Merger") of the Company with and into Sub.  Capitalized terms not otherwise
defined in this Agreement have the meanings defined for them in the
Reorganization Agreement.

     B.  As a condition to the Merger, to preserve the value of the business
being acquired by Parent, the Reorganization Agreement contemplates, among other
things, that the Executive enter into this Agreement effective upon the
Effective Time of the Merger.

     NOW THEREFORE, in consideration of the mutual promises made in this
Agreement, Parent, the Company and the Executive agree as follows:

     1.  Covenant Not to Compete or Solicit.
         ----------------------------------

         (a)  For two (2) years after the termination of Executive's employment
with the Surviving Corporation, Parent or any subsidiary thereof (the "Non-
Compete Period"), the Executive shall not directly or indirectly for himself or
on behalf of or in conjunction with any other person, company, partnership,
corporation, business, group or other entity, without the prior written consent
of Parent, engage anywhere in the world in (whether as an employee, consultant,
proprietor, partner, director or otherwise), or have any ownership interest in
(except for ownership of one percent (1%) or less of the outstanding securities
of an entity whose securities are listed on a national securities exchange), or
participate in the financing, operation, management or control of, any firm,
corporation or business or any business unit of any firm or corporation in any
business selling products or services in direct competition with Parent's or the
Surviving Corporation's business of developing, marketing, maintaining,
supporting or servicing of layout design, mask manufacturing, inspection and
direct-write-on-wafer data preparation software or software applications and
services that enable integrated circuit designers and manufacturers to produce
ICs with subwavelength feature sizes (the "Competing Business"), provided that
                                                                 --------
this Section 1(a) shall not be applicable to the Executive's participation as a
service provider in any division of a firm or corporation which division and
Executive's participation in such division does not relate in any way to the
Competing Business.
<PAGE>

               During the Non-Compete Period, the Executive shall not, directly
or indirectly, without the prior written consent of Parent, (i) solicit,
encourage or take any other action which is intended to induce any employee of
the Surviving Corporation or Parent or any subsidiary thereof to terminate his
or her employment with the Surviving Corporation or Parent or any subsidiary
thereof (as the case may be), or (ii) interfere in any manner with the
contractual or employment relationship between the Surviving Corporation and any
employee of the Surviving Corporation or Parent and any employee of Parent or
any subsidiary of the Surviving Corporation or Parent and any employee of any
such subsidiary (collectively, the "Solicitation Restriction").  Notwithstanding
any other provisions contained herein to the contrary, (i) the last day of the
Non-Compete Period shall in no event be later than the third anniversary of the
effective date of the Merger and (ii) this Agreement shall not be applicable
with respect to the Solicitation Restriction or the Executive's participation as
a service provider or holding an equity interest in any successor entity of the
Company or an entity to which all or substantially all of the assets of the
Company is transferred provided that (a) an Event of Default (as defined in
Section 5 of the Promissory Notes issued pursuant to the Reorganization
Agreement) has occurred and is continuing and (b) the Executive has sought
enforcement of the Security Agreement relating to the Promissory Note held by
Executive.

          (b)  The covenants contained in the preceding paragraphs shall be
construed as a series of separate covenants, one of each county, city and state
of any geographic area where any business is presently carried on by Parent, the
Surviving Corporation or the Company. Except for geographic coverage, each such
separate covenant shall be identical in terms to the covenant contained in the
preceding paragraphs.  If, in any judicial proceeding, a court refuses to
enforce any of such separate covenants (or any part thereof), then such
unenforceable covenant (or such part) shall be eliminated from this Agreement to
the extent necessary to permit the remaining separate covenants (or portions
thereof) to be enforced.  In the event that the provisions of this Section 1 are
deemed to exceed the time, geographic or scope limitations permitted by
applicable law, then such provisions shall be reformed to the maximum time,
geographic or scope limitations, as the case may be, permitted by applicable
laws.

          (c)  The Executive acknowledges that the Executive's covenant not to
compete or solicit contained in this Section 1 is a condition precedent to the
Merger to preserve the value of the business being purchased by Parent pursuant
to the Merger.  The Executive further acknowledges that breach of this Section 1
would cause irreparable injury to Parent and the Surviving Corporation and
agrees that in the event of such breach, Parent and the Surviving Corporation
shall each be entitled to seek injunctive relief without the necessity of
proving actual damages.

     2.   Miscellaneous.
          -------------

          (a)  Severability. If any portion of this Agreement is held by a court
               ------------
of competent jurisdiction to conflict with any federal, state or local law, such
portion of this Agreement shall be of no force or effect and this Agreement
shall otherwise remain in full force and effect and be construed as if such
portion had not been included in this Agreement.

          (b)  No Assignment. The Executive shall not assign this Agreement or
               -------------
any rights or obligations under this Agreement without the prior written consent
of Parent.

                                      -2-
<PAGE>

          (c)  Notice. Any notice or other communication required or permitted
               ------
under this Agreement shall be made in writing and delivered personally to the
other parties or sent by certified or registered mail, return receipt requested
and postage prepaid to the addresses set forth on the signature page hereto or
such other address as any such party shall have furnished to the other parties
in writing in accordance with this Section 2(c).

          (d)  Entire Agreement. This Agreement contains the entire agreement
               ----------------
and understanding of the parties and supersedes all prior discussions,
agreements and understandings relating to the subject matter of this Agreement.
This Agreement may not be changed or modified, except by an agreement in writing
executed by Parent and the Executive.

          (e)  Effectiveness: Term. This Agreement shall become effective upon
               -------------------
the Effective Date and shall continue in full force and effect for three (3)
years from its effectiveness.

          (f)  Other. The waiver of a breach of any term or provision of this
               -----
Agreement shall not operate as or be construed to be a waiver of any other
previous or subsequent breach of this Agreement. This Agreement shall be
governed by the laws of the State of California. All captions and section
headings used in this Agreement are for convenient reference only and do not
form a part of this Agreement. This Agreement may be executed in counterparts,
and each counterpart shall have the same force and effect as an original and
shall constitute an effective, binding agreement on the part of each of the
undersigned.

                                      -3-
<PAGE>

     IN WITNESS WHEREOF, the parties have executed this Agreement as of the date
first above written above.

NUMERICAL TECHNOLOGIES, INC.             EXECUTIVE

By: /s/ Yagyensh C. Pati                 /s/ Kevin MacLean
   --------------------------------      ---------------------------------------
   Name:                                 Name:
   Title:                                Address:
   Address:

TRANSCRIPTION ENTERPRISES LIMITED

By: /s/ Roger Sturgeon
   --------------------------------
   Name:     Roger Sturgeon
   Title:    President
   Address:  16990 Lucky Road
             Los Gatos, CA 95030

TRANSCRIPTION ENTERPRISES, INC.

By: /s/ Yagyensh C. Pati
   --------------------------------
   Name:
   Title:
   Address:

                 [Signature Page to Non-Competition Agreement]

                                      -4-

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